MECH NOTES FOR CLASS 4 PART A

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Q. No

Question

CorrectAnswer

A particle of mass 180 gm has a velocity of 13 m/s. Find its momentum (in kg-m/s)

2.34

Calculate momentum of a body of mass 7 kg moving with a velocity of 24 km/hr

46.667

A body of mass 8 kg falls freely under gravity. Find its momentum ( in kg.m/s) after 6 seconds.

470.88

Find momentum of a train ( in kg.m/s)moving at 65 km/hr, if its weight is 3000 kN.

5521712.5

A truck of mas 1500 kg has a velocity of 36 km/hr. On its way, it hits a car parked by the road side. In doing so, its velocity is reduced to 15 km/hr. Find the momentum ( in kg.m/s) absorbed by the car.

8749.5

A ball of mass 150 gm rolls with a velocity of 2 m/s. It is hit with a bat in the direction of its motion. The velocity changes to 20 m/s. If the bat is in contact with the ball for 0.01 sec, find the impulse ( in kg.m/s)

2.7

A bullet of mass 20 gm leaves the barrel of a gun with muzzle velocity of 600 m/s. If the length of the barrel is 1 m, find the impulse ( in kg.m/s)

A ball of mass 100 gm has initial velocity of 20 m/s. After hitting with a bat, its velocity becomes 30 m/s in the opposite direction. If the ball remains in contact with the bat for 0.006 second, find the impulsive force.

833.333 N

A body of mass 8 kg moves with 4 m/s. Find impulse ( in kg.m/s) required to change velocity to 6 m/s.

Find the force required to produce an acceleration of 3 m/sq. s on a mass of 8 kg.

24 N

A body of mass 18 kg falls freely under gravity. Find the impulsive force after 12 seconds. Take g=9.81 m/sq. s

176.58

A resultant force of 24 N acts on a body of mass 90 kg for a period of 15 seconds. Find the acceleration ( in m/sq. s)produced.

0.2667

A resultant force of 24 N acts on a body of mass 90 kg for a period of 15 seconds. Considering the body to be at rest initially, find the velocity (in m/s) of the body after 15 seconds.

A car of mass 3000 kg has to overcome total frictional and air resistance of 2400 N. Find the force required to produce an acceleration of 0.86 m/sq. s on a level track.

4980

Find the force required to accelerate a block of mass 7 kg at the rate of 0.6 m/sq. s.

4.2 N

A rifle bullet, mass 8 gm has a muzzle velocity of 650 m/s. If the length of the barrel is 1 m, calculate the force accelerating the bullet assuming constant acceleration.

1690 N

A sail boat weighs 8000 N including occupants. The wind exerts a force of 350 N on the boat. The resistance to motion in water is 200 N. Find the acceleration ( in m/sq. s) of the boat. Take g= 9.81 m/sq. s

0.1839

A boat weighing 19620 N is pushed by a force of 120 N. Calculate acceleration ( in m/sq. s)of the boat. Take g= 9.81 m/sq. s

0.06

A boat weighing 19620 N is pushed by a force of 120 N. Calculate the velocity of the boat after 8 minutes if the boat starts from rest.

28.8 m/s

A train weighing 6000 kN running at 54 kmph is brought to rest within a distance of 300 m. Find the force applied by brakes. Take g=9.81 m/sq. s

229.358 kN

An elevator of mass 400 kg starts moving upward with constant acceleration and acquires a velocity of 4 m/s after travelling a distance of 8 m. Find tension in the supporting cable. Take g=9.81 m/sq. s

4324 N

A ball of mass 3 kg moving at 8 m/s strikes another stationary ball of mass 4 kg. If the first ball rebounds with a velocity of 3 m/s, find the velocity ( in m/s) of other ball.

8.25

A sphere of mass 0.8 kg has a velocity of 1 m/s. It strikes another sphere of mass 0.7 kg which is at rest. The impact is direct central. If the first sphere comes to rest after impact, find velocity ( in m/s) of the second sphere.

1.143

A truck of mass 6 tonnes has a velocity 36 kmph. At what velocity ( in m/s) , a truck of mass 4 tonnes will have the same momentum?

A ball of mass 120 g is thrown against a vertical wall with a horizontal velocity of 20 m/s. It rebounds with a velocity of 15 m/s. If the ball remains in contact with the wall for 0.08 second, find the impulsive force.

52.5 N

A gun of mass 50 tonne fires a projectile of mass 450 kg with a horizontal velocity of 600 m/s. If it is resisted by a constant force of 800 kN, find the distance travelled by the gun to come to rest.

0.9113 m

A gun of mass 50 tonne fires a projectile of mass 450 kg with a horizontal velocity of 600 m/s. If it is resisted by a constant force of 800 kN, find the time taken by the gun to come to rest.

0.3375 s

Find the effective force necessary to accelerate a block of mass 5 kg at the rate of 0.007 m/sq. s

0.035 N

A block of mass 8 kg rests on a horizontal surface. Find a constant horizontal force required to give it a velocity of 3 m/s in 2 seconds from start. Take µ = 0.3 , g=9.81 m/sq. s

35.544 N

A rifle bullet of mass 20 g strikes a wooden block with a velocity of 360 m/s. Assuming the constant retarding force of 6480 N, find the distance through which the bullet will penetrate before coming to rest.

200 mm

A lift of mass 980 kg rises with an acceleration of 0.2 m/sq. s. What is the tension in the supporting cable?. Take g=9.81 m/sq. s

9809.8 N

A lift of mass 980 kg rises with an acceleration of 0.2 m/sq. s. How much time does it take to cover a distance of 10 m from start? Take g=9.81 m/sq. s

10 s

An average force of 100 N acts for a time interval of 0.02 seconds on a golf ball that is initially at rest. Calculate the impulse acting on the golf ball.

2 Ns

A 2000 kg car collides with a 1500 kg car that was initially at rest. The two cars lock together and move off after the collision at a speed of 6 m/s. Calculate the speed of the 2000 kg car before the collision.

10.5 m/s

A body of mass 8 kg falls freely under gravity. Find its momentum after 6 seconds in kg m/s

470.88

A body of mass 18 kg falls freely under gravity. Find the impulsive force after 12 seconds in Newton.

176.58

The velocity of the car moving in a straight line increases from 8 m/s to 22 m/s in 7 seconds. What is the average acceleration of the car during this period?

2 m/sq.s

A ball of mass 0.6 kg is located at the top of a hill of height 8 m. If friction can be neglected, calculate the speed of the ball at the bottom of the hill if the ball is released from rest. Take g = 9.8 m/sq. s

12.52 m/s

A flywheel is rotating at 110 rpm. Calculate its velocity in degrees/s

660

A flywheel is rotating at 110 rpm. Calculate its velocity in radians /s.

11.519

A car is moving with a uniform velocity of 72 kmph. The diameter of the wheel is 60 cm. Find the rpm of the wheel.

636.62

A car is moving with a uniform velocity of 72 kmph. The diameter of the wheel is 60 cm. If the car moves for 2 minutes with this velocity, find the angular distance moved by the wheel.

1273.239

A cylindrical piece 15 cm in diameter rotates in a lathe at 750 rpm. Calculate the linear velocity (in m/s) of a point on the surface of the cylinder.

5.89

A wheel 800 mm diameter starts from rest and accelerates uniformly. After 24 seconds, it attains angular velocity of 120 rad/s. Find the angular acceleration (rad/sq. s)

A wheel 800 mm diameter starts from rest and accelerates uniformly. After 24 seconds, it attains angular velocity of 120 rad/s. Find the total angle turned through ( in revolutions).

229.183

A body accelerating uniformly at 5 rad/sq.s is found to be rotating at 90 rad/s at the end of 12 seconds. Determine its initial velocity ( in rad/s)

A body accelerating uniformly at 5 rad/sq.s is found to be rotating at 90 rad/s at the end of 12 seconds. Determine the angle turned during this interval.

720 rad

At the end of 20 seconds, a flywheel reaches a speed of 15 rad/s starting from rest. If the angular acceleration is uniform, find the angular displacement during sixteenth second.

11.625 rad

A flywheel rotating at 1000 rpm slows down uniformly to 500 rpm completing 500 revolutions during this retardation. Find total time of retardation

39.969 s

A flywheel rotating at 1000 rpm slows down uniformly to 500 rpm completing 500 revolutions during this retardation. Find rate of retardation (rad/sq. s).

-1.31

A wheel of diameter 100 mm rotates with 150 rpm and comes to rest in 10 seconds. Calculate linear velocity ( in m/s) of a point on the rim of the wheel.

0.7853

A wheel of diameter 100 mm rotates with 150 rpm and comes to rest in 10 seconds. Calculate linear acceleration ( m/sq. s) of a point on the rim of the wheel.

-0.0785

A flywheel starting from rest under uniform acceleration completes one revolution in eighth second. Find angular velocity ( in rev/s) after 15 seconds from start.

A flywheel starting from rest under uniform acceleration completes one revolution in eighth second. Find angular acceleration ( rev/sq. s) after 15 seconds from start.

0.1333

A pipe of cross sectional area 80 sq. cm has a constriction where the area is reduced to 20 sq. cm. If the velocity of the fluid in the larger area is 0.3 m/s, what is the velociy of the fluid in the constricted region?

1.2 m/s

A horizontal force of 300 N displaces a body on horizontal surface by 4 m. Calculate Work Done.

1200 J

A locomotive pulls a train with a uniform velocity of 54 kmph and exerts a tractive force of 15 kN. Find the work done by the locomotive in 90 minutes.

1215000 kJ

Calculate the work done in pulling a block of wood 400 kg for length of 7m up a smooth inclined plane which makes 40 degrees with the horizontal.

17656.09 J

A water tank 6x4x3 m is full of water. The bottom of tank is on ground level. Find work done in emptying the tank. Take density of water=1000 kg/cu. m and value of g=9.81 m/sq. s.

1059.48 kJ

A trolley weighing 3000 N moves over a level track for a distance 1800 m. the resistance of the track is 4.5 N per 1000 N. Find the work done.

24.3 kJ

A block of 30 kN is placed on 30 degree inclined plane. If coefficient of friction is 0.3. Find the work done in moving the block through 2m up the plane by applying a force parallel to plane.

45.588 kJ

A force acting on a body gradually increases from 0 to 80 N and displaces it through 15 cm. Find the work done.

6 J

The springs of a chest expander are 600 mm when unstretched. They are stretched to 700 mm by applying a force which varies at the rate of 0.5 N per mm of stretch. Find the work done in stretching.

2.5 J

A 20m long cable weighing 30 N/m is suspended from a drum. How much work is done in winding 15 metres length of this cable on the drum?

5625 J

A steamer runs at a constant speed of 27 km/hr and requires a force of 50 kN to overcome water and other resistances. Find the power developed.

0.375 MW

A water tank 20000 litre capacity is to be filled in 30 minutes by a pump. For this purpose, water is to be lifted through average height of 15 m. If the efficiency of the pump is 60%, find the rated power of the pump.

2.725 kW

How many litres of water can be lifted in 15 minutes to a height of 18 m by a pump of 75 kW? Efficiency= 80%.

305.8 x 10 exp(3) ltrs

A man weighing 600 N climbs a staircase of 12 m height in 30 seconds. How much power was consumed?

0.24 kW

Find power of a pump to fill water tank 3m x 2m x 1.5m in 45 minutes. The water is to be lifted through 12 m height. Assume efficiency of pump= 85%.

461.647 W

A train weighing 400 kN is moving on a straight horizontal track at a uniform speed of 45 kmph. The track offers a resistance of 8N per 1000 N. Find power required by engine.

0.04 MW

The power of the machine is 10 kW. Find the time taken ( in seconds) to lift a body of mass 1000 kg to a height of 20 m.

19.62

A lift of total weight of 6 kN is going up at 5 m/s. Find the power utilized in kW.

30 kW

Power of a pump is 5 kW. Find the time ( in seconds) required to raise water to an average height of 15 m and fill an elevated tank of 80,000 lit. capacity.

2354.4

A body of mass 120 kg is at a height 3m above datum. Find its potential energy.

3531.6 J

Find potential energy possessed by a body of 600 N at a height of 4 m.

2.4 kJ

A stone falls from a certain height and strikes the ground with velocity 8 m/s. the mass of the stone was 1.5 kg. What potential energy, the stone has when it was at that height? Take g = 9.81 m/sq. s

48 J

A mass of 5 kg is moving with a velocity of 3 m/s. Find its kinetic energy.

22.5 J

A vehicle is moving with a velocity of 36 km/hr. If weight of the vehicle is 6 kN, find its kinetic energy. Take g = 9.81 m/sq. s

30581 J

A bowler throws a ball with a speed of 20 m/s. The moment the ball touches the ground, it looses its energy by 12 Joule. Calculate the speed (m/s) at which it hits the bat. Neglect air and other resistances. Mass of the ball is 200 gms.

16.733

A body weighing 280 N is at a height 10 m above ground level and moving with a velocity 1.6 m/s. Calculate total energy ( in Joules) possessed by the body. Take g = 9.81 m/sq. s

2836.53

A body of mass 1.2 kg moving in space with a velocity of 280 m/s is at a particular height of 75 m from the ground. Calculate kinetic energy ( in Joules) of the body.

47040

A body hits the floor with a velocity of 18 m/s and bumps back. The weight of the body is 22 N. The loss of energy due to hit is 45 N-m. Calculate the velocity of the bump in m/s. Take g = 9.81 m/sq. s

16.849

A pull of 60 N at 25 deg. up the horizontal is required to just move a block of weight(W). Calculate the weight of the block if µ = 0.25

242.871 N

A body weighing 200 N is resting on a horizontal surface. It is just on the point of moving when a horizontal force of 50 N is applied on it. Find coefficient of friction.

0.25

A block weighing 800 N resting on a horizontal surface can be moved by a pull of 300 N force applied at an angle of 30 deg. with the horizontal. Find coefficient of friction.

0.4

A block of 100 N is kept on 30 deg. inclined plane. Find the force applied parallel to the plane, required to just move the block up the plane. Take coefficient of friction =0.4

84.641 N

A 40 kN block on 24 deg. inclined plane requires a force of 22 kN to move it up the plane. If the applied force is in the direction of plane, find coefficient of friction between the block and plane.

0.1568

A block of 60 kN is kept on 45 deg. inclined plane. If coefficient of friction is 0.2, find the force ‘p’ applied parallel to plane to just prevent the block from sliding down.

33.941 kN

A 500 N block kept on 30 deg. requires a force of 150 N applied parallel to plane to just prevent it from sliding the plane. Find coefficient of friction.

0.2309

A body of weight 300 N is lying on a rough horizontal plane having coefficient of friction as 0.3. Find the magnitude of the force, which can move the body while acting at an angle of 25 deg. with the horizontal.

87.117 N

A body of weight 500 N is lying on a rough plane inclined at an angle of 25 deg. with the horizontal. It is supported by an effort parallel to the plane. Determine the minimum value of p, for which the equilibrium can exist, if the angle of friction is 20 deg.

46.375 N

Find the horizontal force required to drag a body of weight 100 N along a horizontal plane. If the plane, when gradually raised up to 15 deg, the body will begin to slide.

26.79 N

A body of weight 50 N is hauled along horizontal plane by a pull of 18 N acting at an angle of 14 deg. with the horizontal. Find the coefficient of friction.

0.383

A man is walking over a dome of 10 m radius. How far can he descend from the top of the dome without slipping? Take coefficient of friction between the surface of the dome and shoes of the man as 0.6.

31 deg.

A force of 250 N pulls a body of weight 500 N up an inclined plane, the force being applied parallel to the plane. If the inclination of the plane to the horizontal is 15 deg., find the coefficient of friction.

0.25

A screw jack has mean diameter of 50 mm and pitch 10 mm. if the coefficient of friction between its screw and nut is 0.15, find the effort required at the end of 700 mm long handle to raise a load of 10 kN.

0.0766 kN

If a car starts from rest with an acceleration of 4.5 m/sq. s. Find the velocity after 15 seconds.

67.5 m/s

If a car starts from rest with an acceleration of 4.5 m/s2. Find the distance travelled after 15 seconds.

506.25 m

The momentum of the body is 32000 kg m/s. If the velocity of the body is trippled and mass is doubled, what is its final momentum?

192000 kg m/s

100

At the certain instant, velocity of the car is 20 m/s. If the car accelerates at the rate of 0.2 m/sq.s, how much time it will take to cover a distance of 2000 m.

73.205 s

101

A scooter has an initial velocity of 4 m/s. It accelerates for 12 seconds at the rate of 0.25 m/sq. s. Determine the final velocity after 12 seconds

7 m/s

102

A scooter has an initial velocity of 4 m/s. It accelerates for 12 seconds at the rate of 0.25 m/sq. s. Determine the distance travelled during the time.

66 m

103

A train starts from rest and accelerates at the rate of 1.2 m/sq. s. Calculate its velocity in km/hr at the end of 375 metres.

108

104

A jeep travelling with a velocity of 90 km/hr is brought to rest in 20 seconds with uniform retardation by applying brakes. Determine the retardation after the brakes are applied.

1.25 m/sq.s

105

A jeep travelling with a velocity of 90 km/hr is brought to rest in 20 seconds with uniform retardation by applying brakes. Determine the distance travelled after the brakes are applied.

250 m

106

A vehicle moving with certain velocity decelerates uniformly at the rate of 1.5 m/sq. s for 48 m and attains a velocity of 5 m/s. Find its initial velocity

13 m/s

107

A vehicle moving with certain velocity decelerates uniformly at the rate of 1.5 m/sq. s for 48 m and attains a velocity of 5 m/s. Find time of journey

5.333 s

108

An aeroplane starting from rest covers a run away of 700 metres in 15seconds and then takes off. With what velocity in km/hr does it take off? Assume constant acceleration.

336

109

A body starts from rest with a constant acceleration of 0.5 m/sq. s. After what time its velocity be 2.5 m/s?

5 s

110

A body starts from rest with a constant acceleration of 0.5 m/sq. s. How much distance it will travel when its velocity becomes 2.5 m/s?

6.25 m

111

If two forces F1 = 120 N and F2=80 N are acting at a point making an angle of 55 deg. between them. Find the resultant of these forces in magnitude.

178.361 N

112

The block of weight 224 N is resting on a rough plane inclined at an angle of 15 deg. to the ground. If coefficient of friction between the block and the plane is 0.24, find the force required parallel to the plane to just move the block.

109.904 N

113

100 m long wire has diameter of 2 cm. How much load needs to be suspended from the wire if change in length should be 0.3 mm. Youngs modulus of wire is 200 x 10 exp(9) N/sq. m. Take value of ∏= 3.142

188.496 N

114

A tank with a floor size of 9m x 8m contains fresh water of density 1000 kg/cu. m to a depth of 4 m. Calculate the force on the long side of the tank. Take g=9.81 m/sq. s

706.32 kN

115

2 g of oil of relative density 0.8 is mixed with 4 g of another oil of relative densiy 0.9. Find te relative dennsity of the mixture.

0.864

116

A pull of 80 N at 300 up the horizontal is required to just move a lock of weight (W). Calculate the wight of the block if µ = 0.25

317.128 N

117

A body weighing 240 N is resting on a horizontal surface. It is just on the point of moving when a horizontal force of 60 N is applied on it. Find coefficient of friction.

0.25

118

A body weighing 240 N is resting on a horizontal surface. It is just on the point of moving when a horizontal force of 60 N is applied on it. Find angle of friction.

14.036 deg.

119

A block weighing 1000 N resting on a rough inclined surface can be moved by a pull of 400 N force applied at an angle of 30 deg. with the horizontal. Find coefficient of friction.

0.433

120

A body weighing 1500 N is resting on a rough horizontal plane. A pull of 300 N applied at 30 deg. up with respect to horizontal just move the body. Find coefficient of friction.

0.192

121

A 60 kN block on 20 deg. inclined plane requires a force of 40 kN to move it up the plane. Find coefficient of friction between the block and plane.

0.345

122

An automobile accelerates uniformly from rest to 95 km/hr in 28 seconds. Find its acceleration ( in m/sq.s)during this time.

0.942

123

An automobile accelerates uniformly from rest to 95 km/hr in 28 seconds. Find its displacement during this time.

369.264 m

124

A train changes its speed uniformly from 100 to 50 km/hr in a distance of 500 m. What is its acceleration ( in m/sq. s)?

-0.579

125

A balloon is rising with a velocity of 2 m/s when a bag of sand is released. If its height at the time of release is 100 m, how does it take for the sand to reach the ground? Take g=9.81 m/sq. s

4.724 s

126

A ball is projected vertically upward with a velocity of 24 m/s. Two seconds later, a second ball is projected vertically upward with a velocity of 18 m/s. at what point above the surface of the earth will they meet? Take g=9.81 m/sq. s

16.205 m

127

A flywheel 1.2 m in diameter accelerates uniformly from rest to 2000 rpm in 20 seconds. What is angular acceleration ( in rad/sq.s)?

10.472

128

How many revolutions does the flywheel make in attaining its speed of 2000 rpm?

333.334

129

A wheel 200 mm in diameter comes to rest from a speed of 800 rpm in 600 seconds. Determine the angular acceleration ( in rad/sq.s).

-0.14

130

A wheel accelerates uniformly from rest to a speed of 200 rpm in 1/2 seconds. It then rotates at that speed for 2 seconds before accelerating to rest in 1/3 seconds. How many revolutions does it make during the entire time interval?

8.056

131

An automobile travels a distance of 370 km in a period of 7 hours. Determine the average velocity of the vehicle in m/s.

14.683

132

If a body moves at the rate of 45 kmph for 6 min, then 90 kmph for 10 min and finally 8 kmph for 3 min, what is the average velocity ( in m/s) in the total interval?

17.456

133

A car travels along a straight track between two points at a mean speed of 60 m/s. It returns at a mean speed of 40 m/s. What is the mean speed for the round trip ( in m/s)?

134

An automobile accelerates uniformly from rest to 72 kmph and then the brakes are applied so that it decelerates uniformly to a stop. If the total time is 15 seconds, what distance was travelled?

150 m

135

A bullet is fired with a muzzle velocity of 600 m/s. if the length of the barrel is 750 mm, what is the average acceleration?

240 km/sq.s

136

An automobile is decelerating from a speed of 65 kmph at the rate of 1.5 m/sq.s. How long will it take to come to rest?

12.037 s

137

An automobile is decelerating from a speed of 65 kmph at the rate of 1.5 m/sq.s.How far will it have gone before coming to rest?

108.721 m

138

A stone is dropped from a balloon that is ascending at a uniform rate of 10 m/s. If it takes the stone 10 seconds to reach the ground, how high was the balloon at the instant the stone was dropped? Take g=9.81 m/sq. s

390.5 m

139

A man in a balloon rising with a constant velocity of 4 m/s propels a ball upward with a velocity of 1.2 m/s relative to the balloon. After what time interval will the ball return to the balloon? Take g=9.81 m/sq. s

0.245 s

140

A stone is dropped with zero velocity into a well. The sound of the splash is heard 3.63 seconds later. How far below the ground surface is the surface of the water? Assume the velcoity of sound is 331 m/s. Take g=9.81 m/sq. s

58.49 m

141

Boy A throws a ball vertically up with a velocity of 9 m/s from the top of a shed 2.5 m high. Boy B on the ground at the same instant throws a ball vertically up with a speed of 12 m/s. Determine the time at which the two balls will be at the same height above the ground. Take g=9.81 m/sq. s

0.833 s

142

Boy A throws a ball vertically up with a velocity of 9 m/s from the top of a shed 2.5 m high. Boy B on the ground at the same instant throws a ball vertically up with a speed of 12 m/s. What is the height at which the two balls will be at the same height above the ground. Take g=9.81 m/sq. s

6.596 m

143

Body A starts from rest at point 'O' and travels along a straight line with an acceleration of 2 m/s. Body B satrts from rest at 'O' 4 seconds later and travels along the same path with an acceleration of 3 m/sq.s. How far from 'O' will they be when B overtales A?

475.153 m

144

A radar equipped police car notes a car travelling 110 km/hr. The police car starts pursuit 30 seconds after the observation and accelerats to 160 km/hr in 20 seconds. Assuming the speeds are maintained on a straight road, how far from the observation post will the chase end?

3.913 km

145

An Automobile accelerates uniformly fro rest on a straight level road. A second automobile starting from the same point 6 seconds later with initial velocity zero accelerates at 6 m/sq.s to overtake the first automobile 400 m from the starting point. What is the acceleration of the first automobile?

2.598 m/sq.s

146

A particle of dirt falls from an elevator that is moving up with a velocity of 3 m/s. If the particle reaches the bottom in 2 seconds, how high above the bottom was the elevator when the particle started falling?

13.62 m

147

A bullet is fired vertically upward with a velocity of 660 m/s. Theoretically to what height will the bullet ascend?

22.202 km

148

A ball is thrown vertically upward with a speed of 9 m/s from the edge of a cliff 15 m above sea level. What is the highest point above sea level reached?

19.128 m

149

A ball is thrown vertically upward with a speed of 9 m/s from the edge of a cliff 15 m above sea level. How long does it take to hit the water?

2.892 s

150

A ball is thrown vertically upward with a speed of 9 m/s from the edge of a cliff 15 m above sea level. With what velocity does it hit the water?

19.372 m/s

151

The wheels of an automobile are 750 mm in diamter and have an angular speed of 17 rad/s. What is the speed of the automobile in km/hr?

22.95 km/hr

152

The flywheel of an automobile acquires a speed of 200 rpm in 45 seconds. Find its angular acceleration. Assume uniform motion.

4.654 rad /sq. s

153

A cylindrical well is 2 m in diameter and 12 m deep. If there is 3 m of water in the bottom of the well, determine the work done in pumping all this water to the surface. Take g = 9.81 m/sq. s

970.799 kN-m

154

A cylindrical well is 2 m in diameter and 12 m deep. If there is 3 m of water in the bottom of the well. What work must be done by a pump that 60% efficient? Take g = 9.81 m/sq. s

1617.998 kN-m

155

A man, who can push a force of 265 N, wishes to roll a barrel of 90 kg into a truck which is 1 m above ground. How long board must he use ?

3.332 m

156

A man, who can push a force of 265 N, wishes to roll a barrel of 90 kg into a truck which is 1 m above ground. How much work will he do in getting the barrel into the truck?

882.9 N-m

157

A 5 kg block slides 2.5 m on a horizontal surface. If the coefficeint of friction is 0.3, what work is done by the block on the surface?

0 J

158

A 5 kg block slides 2.5 m on a horizontal surface. If the coefficeint of friction is 0.3, what work is done by the surface on the block?

36.788 J

159

The 8 kg block is acted upon by a push of 100 N force making an angle of 20 deg with the horizontal. If the coefficient of sliding friction is 0.3, determine the work done by all forces as the block moves 4 m.

240.657 J

160

A 5 kg block slides 2 m down a plane inclined 40 deg. with the horizontal. Determine the work done by all forces acting on the block. The coefficient of slidng friction is 0.40

32.998 J

161

A force of 900 N is required to compress a spring through a distance of 100 mm. if the force required to compress the spring varies directly with its deformation, how much work is done in compressing it through 225 mm?

227.813 J

162

An automobile of mass 1150 kg climbs a 10% grade at a uniform rate of 24 km/h. If the resistance is 88 N/tonne, what power is the car developing?

8.1589 kW

163

A Steam engine raises an 1800 kg mass vertically at the rate of 9 m/s. What is the power of the engine assuming an efficiency of 70%?

227.031 kW

164

A 50 kg homogenous cylinder 1200 mm in diameter is rotating at 100 rpm. A torque of 30 N-m is needed to keep this speed constant ( overcoming friction). What power is required?

314.159 W

165

A 100 g body falls from 1500 mm to the surface of the earth. What is its kinetic energy as it hits the ground?

1.472 J

166

A bullet enters a 50 mm plankwith a speed of 600 m/s and leaves with a speed of 240 m/s. Determine the greatest thickness of plank that could be penetrated by the bullet.

59.524 mm

167

A block of mass 35 kg is acted upon by a 130 N horizontal force. If the coefficient of friction is 0.25, determine the speed of the block after it has moved 6 m from rest.

3.892 m/s

168

A 60 g bullet moving with a sped of 500 m/s strikes a 5 kg block moving in the same direction with a speed of 30 m/s. What is the resultant speed of the bullet and the block assuming the bullet to be embedded in the block?

35.573 m/s

169

A 50 kg mass falls freely from rest for 4 seconds. Find its momentum at that time.

1962 kg-m/s

170

A pile driver hammer and of mass 450 kg is dropped from a height of 7.5 m. if the trime required to stop the pile driver is 1/20 second, determine the average force actng during that time.

109.175 N

171

A body is thrown upward with an initial speed of 15 m/s. Find the time required for the body to attain a speed of 6 m/s downward.

2.141 s

172

A 32 kg boy is standing in a 45 kg boat that is initially at rest. If the boy jumps horizontally with a speed of 2 m/s relative to the boat, determine the speed of the boat.

0.831 m/s

173

A 900 kg car travelling 48 km/h couples to a 680 kg car travelling 24 km/h in the same direction. What is their common speed after coupling?

10.464 m/s

174

A 900 kg car travelling 48 km/h couples to a 680 kg car travelling 24 km/h in the same direction. What is the loss in kinetic energy?

8609.827 J

175

What should be the perpendicular force component of a ramp at an angle 40 deg. to the ground in order to withstand a car exerting a force of 1500 N?

1149.067 N

176

An object weighs 10 kg is hanging down from a vertical cable made of iron. Calculate the acceleration that the object is generating if tension in the rope is 150 N. Take g= 9.81 m/sq. s

5.19 m/sq.s

177

Calculate the tangential velocity of an object attached to string of length 2 m that rotates with a frequency of 7 rps

88 m/s

178

A ball thrown vertically up returns to its start point in 7 seconds. Find its initial speed. Take g = 9.81 m/sq.s

34.335 m/s

179

A car is involved in a collision in which it is brought to a stand still from a speed of 31 m/s. The driver of mass 65 kg is brought to rest by his belt in a time of 360 milliseconds. Calculate the ratio of the force exerted by the seat belt on the driver to the weight of the driver.

8.778

180

The momentum of a motorcycle is 32000. Calculate the momentum of the motorcycle if its velocity is trippled. If its mass is doubled.

96000

181

The momentum of a motorcycle is 32000. Calculate the momentum of the motorcycle if its mass is doubled.

64000

182

A car starts accelerating from rest with an acceleration of 2.5 m/sq. s. at the same time, a bus moving with constant speed of 16 m/s overtakes it in a parallel plane. Calculate the speed of car as it overtakes the bus.

204.8 m

183

A car starts accelerating from rest with an acceleration of 2.5 m/sq. s. at the same time, a bus moving with constant speed of 16 m/s overtakes it in a parallel plane. Calculate the distance travelled by car before it overtakes the bus.

32 m/s

184

Calculate the force required to stretch 2 cm diametersteel rod by 0.3%. Assume Y=200 GPa and ∏ = 3.14

188.4 kN

185

Initial momentum = 23.1 kg. Mmentum after collision = 42.9 kg-m/s. Time 5 seconds. Find force on body due to collision.

3.96 N

186

If an object weighs 3 gms on earth, what is the mass on Moon. Assume that the gravity on Moon is one sixth of that on Earth.

3 gms

187

Ball A is thrown vertically up from the ground at time t =0 with an initial velocity of 55 m/s. Ball B is thrown vertically up from ground at time t=4 seconds with initial velocity of 45 m/s. Calculate the distance between the two balls when t=8 seconds.

24.56 m

188

Two cars A and B start from same point. Car A moves North and Car B moves South. Car A starts from rest and accelerates with 3 m/sq. s for 6 seconds and then moves with constant velocity. Car B starts from rest and moves with an acceleration of 4 m/sq. s for 5 seconds and then moves with uniform velocity. At an instant,distance between cars is 1074 m. Calculate time ( that has passed since two cars started moving) when measurement was taken.

31 seconds

189

A machine gun fires 320 bullet per minute. Mas of bullet=40 gms. Velocity = 480 m/s. Calculate power of gun.

24.576 kW

190

Magnitude of resultant force of two vector of equal magnitude = 1/3 magnitude of the force. Find the angle between the forces.

160.81 deg.

191

The dispacement 'S' in metres of a body varies with time 't' ( seconds) as S=-2/3 sqr(t) + 16(t) + 2. How long does the body take to come to rest.

12 seconds

192

A turbo propelled car starts from rest x=0 and moves in direction of x with constant acceleration of 4 m/sq.s, 10 seconds until the turbo fuel is exhausted and continue with constant velocity. Calculate distance covered by car in 14 seconds.

360 m

193

A tank 6 X 4 X 3 m full of water. Bottom is @ ground level. Find the work done in emptying the tank. Take density = 1000 kg /cu.m and g= 9.81 m/sq. s

1.059 MJ

194

A tank with a floor size of 6m X 6m contains fresh water ( density = 1000 kg/cu.(m)) to a depth of 7 m. Calculate force on side of tank.

1.442 MN

195

A boy weighs 326 N normally. When the boy jumps up, the scale shows a reading of 410 N at the instant that he jumps up. Estimate the boy's max acceleration ( g = 10 m/sq. s)

12.577 m/sq.s

196

A fluid is flowing with a velocity of 3.6 m/s. If the density offluid is 2.3 gm/sq. cm, calculate K.E./sq. m

14.904 kJ

197

A bullet travelling with a velocity of 520 m/s strikes a freely suspended block of mass 18 kg and gets embedded in it. Mass of bullet is 60 gms. What is the velocity with which block swings?

1.728 m/s

198

A cricket ball is thrown at a speed of 40 m/sin the direction of 45 deg. above horizontal. g = 9.8 m/sq. sCalculate the time taken by ball to return to ground.

5.772 s

199

A particle moving along x-axis has a velocity V(t ) = 12(t)-1.95(sq(t)). Find its acceleration at t = 9 seconds

-23.1 m/sq.s

200

A car starts accelerating from rest with acceleration of 1.4 m/sq. s. At the same instant, a bus moving speed of 12 m/s passes along parallel line. How long does car take to overtake bus. Also, find distance travelled.

205.714 m

201

Two balls are dropped from different height. One is dropped two seconds later but they both strike the ground at the same time ( ie. ) 5 seconds after first is dropped. If the difference in their height is 78 m, what height the second was dropped from. Take g = 10 m/sq.s

47 m

202

A force of 336.6 N applied parallel to the plane is required to move a body of 500 N up the plane. Coefficient of friction = 0.2. Find angle of inclination

30 deg

203

Calculate the moment of inertia of a spherical shell of radius 8 cm and mass 12 kg

0.0512 kg-sq(m)

204

A gear wheel with 50 teeth is driven by another wheel with 100 teeth at 250 rpm. Find the speed of driven wheel?

500 rpm

205

A box slides down on incline with a uniform acceleration. It starts from rest and attain a speed of 5.4 m/s in 9 seconds. Find the average velocity of box between t=2 seconds and t=5 seconds

2.1 m/s

206

A wire is stretched by 20 mm by a force of 0.69 kN. How much work is done in stretching the wire?

6.9 J

207

A 5.4 kg mass is suspended by a spring whose constant is 19.6 N/cm. Calculate the elongation of spring ( g= 9.8 m/sq.s )

2.7 cm

208

A bullet of mass 40 gms travelling upwards strikes a freely suspended 13 kg block @ speed of 640 m/s and gets embedded in it. Calculate the height, block raises above its initial position. Take g = 9.81 m/sq. s.

0.196m

209

A body is travelling with a velocity of 100 m/s and a deceleration of 5 m/sq.s . How much distance does the body travel before it comes to rest. Assume negligible friction.

1000 m

210

A rod can support a maximum load of 3200 N before exceeding its elastic limit. Calculate the diametyer of the rod. Assume the stress for elastic limit = 480 Mpa. Assume pi= 3.14

2.914 mm

211

What is the Kinetic energy of an object weighing 50 gm with angular velocity = 20 rad/s hanging from a string of 3 m?

90 J

212

Two cars A & B start from rest at the same time and same point. Car A movs North with an acceleration of 5 m/sq. sfor 5 seconds and then moves at a uniform velocity. Car B moves South with acceleration of 4 m/sq.s for 8 seconds and then moves at uniform velocity. Calculate the distance between both the cars after 20 seconds of start.

949.5 m

213

An Auto travels at a rate 45 kmph fr 6 min, then 60 kmph for 6 min and finally at 30 kmph for 8 min. Find total distance in km and average speed in kmph.

43.5 kmph

214

A body of mass 10 kg experiences a constant force of 8 N for a period of 4 seconds. After this, experiences a frictional force that causes a deceleration of 0.5 m/sq. s. Assume that the body is initially at rest when the initial force starts to act on it. Calculate the time taken by body to come to rest

10.4 s

215

A bullet travelling with a velocity of 380 m/s strikes a freely suspended block of mass 17 kg and gets embedded in it. Mass of bullet is 75 gms. Calculate the quantity of K.E. of the bullet that will be converted into internal energy in kJ?

5.391 kJ

216

A bullet weighing 50 gms fired from a gun travels with a velocity of 100 m/s. It hits a block weighing 200 gms moving with a speed of 40 m/s. Calculate the velocity with which both the objects travel after bullet hits the block. Assume that bullet and block travel at same speed.

52 m/s

217

A body of mass 8 kg experiences a constant forceof 4 N. Assume that body is initially at rest when the force starts to act on it. What is the final velocity of body after 10 seconds?

5 m/s

218

A car which is moving with a velocity of 36 m/s is met with an accident. The driver of mass 92 kg is brought to rest by his seat belt in 500 milliseconds. Calculate the average force exerted on driver by his seat belt.

6.624 kN

219

A vehicle velocity increases uniformly from 4 m/s to 15 m/s while covering a distance of 50 m. Find the acceleration at time to cover distance.

2.09 m/sq. s

220

An object is moving along the straight line with its displacement S= t^3 - 4t^2 + 17t-60 where displacement is in m and t in seconds. Calculate the displacement of an object when acceleration=0.

-42.074 m

221

Normal weight of a boy is 25 kg. When boy jumps, scale shows reading of 390 N at the instant he jumps up. Estimate maximum acceleration. Take g=9.81 m/sq.s

15.6 m/sq.s

222

A Ship racing due South at 12 knots runs into a 5 knot current moving South East. Find resultant speed of ship in knots.

15.933

223

A load of 224 N rests on a plane inclined at 15 deg. to horizontal. Coefficient of friction between load and plane = 0.24. Calculate force required to pull load.

109.9 N

224

Bullet of mass 400 gms has constant velocity= 45 kmph. When it reverses direction, what is momentum in kg-m/s

-10

225

The position of an object moving along x-axis is given by x=6-4t+5t^2, where t is in seconds. Find average velocity between t=2 seconds and t = 5 seconds

31 m/s

226

A train is 600 m long and passes a car within 10 seconds. Car speed is 72 kmph. Find speed of train.

288 kmph

227

A force of 1200 N compresses a spring from its natural length 18 cm to 16 cm. Calculate the Work Done in compressing it from 16 cm to 14 cm

36 J

228

A man runs 5 m in 12 seconds according to the relationship s= t^4 + 2t^2 - . Find velocity of man after 7 second.

0.3329 m/s

229

From top of a building 40 m tall, a boy projects a stone vertically up with initial velocity 10 m/s such that eventualy it falls to ground. After how long will the stone strike the ground? Take g= 9.81 m/sq.s

4.052 s

230

Find the 2nd moment of area of rectangle( in m^4) of width 10 m and depth 5 m about its centroid.

104.167

231

The dimension of a rectangular block in order ( l, b, h) are 3.71, 1.14 and 2.65, uncertainty of the measurement = +/-0.01. Calculate the maximum volume

11.379

232

The dimension of a rectangular block in order ( l, b, h) are 3.71, 1.14 and 2.65, uncertainty of the measurement = +/-0.01. Calculate the minimum volume

11.038

233

A 45 N weight is dropped on a pan 450 mm below it. Pan is mounted on spring ( K=1800 N/m). Assume impact to be perfectly plastic, weight of pan (w)= 113 N. Determine velocity of the weight and pan immediately after impact.

2.971 m/s

234

A 45 N weight is dropped on a pan 450 mm below it. Pan is mounted on spring ( K=1800 N/m). Assume impact to be perfectly plastic, weight of pan (w)= 113 N. Determine maximum compression of spring when system comes to rest

0.1268 m

235

What increase in pressure is required to decrease the volume of 220 ltr of water by 0.004%. Initial pressure =2100 Mpa

0.084 Mpa

236

A runner travels 1.75 laps around the track in 70 seconds. Diameter of track = 35 m. Find average speed of runner. Take ∏= 3.142

2.749 m/s

237

A body with velocity 8 m/s moves a long a straight line with constant acceleration and travels 500 m in 20 seconds. Calculate the average speed of the body during the time period.

25 m/s

238

A body with velocity 8 m/s moves a long a straight line with constant acceleration and travels 500 m in 20 seconds. Calculate the final velocity of the body during the time period.

42 m/s

239

A body with velocity 8 m/s moves a long a straight line with constant acceleration and travels 500 m in 20 seconds. Calculate the acceleration of the body during the time period.

1.7 m/sq.s

240

A 10 kg object travelled at a speed of 50 m/s on a frictional pad. Calculate the magnitude of force that should be applied on the object to stop within 10 m.

1250 N

241

Calculate moment of Inertia of solid sphere of radius 8 cm and mass 12 kg.

0.031 kg. sq(m)

242

What is the force on body sliding over an inclined plane making an angle of 45 deg. Weight of body = 20 kg. Coefficient of friction = 0.75

34.684 N

243

Two boys started running straight towards each other from two points that are 200 m apart. The first boy starts running with a uniform speed of 6 m/s. The second boy starts one second later with uniform speed of 8 m/s. Calculate time with first boy runs before they meet.

14.857

244

110.856 m

245

K of solid disc wheel of uniform thickness is r/sqrt(2) from centre, where r is radius of wheel. Calculate K.E. in kJ in a solid dsic wheel of 1400 mm dia and 1250 kg mass, when its speed changes from 8∏ to 10 ∏ rad /s.

3022.566 J

246

A ball is dropped from top of a building. The ball takes 0.5 seconds to pass the 3 m length of window some distance from top of the building. How fast was the ball going to pass the top of the window? Take g=9.8 m/sq.s

3.548 m/s

247

An elevator lifts 10 m in 3 seconds, mass of elevator = 30 kg. Find tension. Take g= 9.81 m/sq. s

360.96 N

248

Ball A is thrown vertically up from the ground at time t =0 with an initial velocity of 60 m/s. Ball B is thrown vertically up from ground at time t=0 seconds with initial velocity of 45 m/s. Calculate the maximum distance between the two balls. Take g=10 m/sq.s

135 m

249

Ball A is thrown vertically up from the ground at time t =0 with an initial velocity of 60 m/s. Ball B is thrown vertically up from ground at time t=0 seconds with initial velocity of 45 m/s. Calculate the time when the distance between the two balls is maximum. Take g=10 m/sq.s

9 s

250

A cricket ball is thrown at a speed of 40 m/s in the direction of 45 deg. above horizontal. g = 9.81 m/sq. s. Calculate the maximum height of the ball before it returns to ground.

40.775 m

251

A Brass object is suspended by a wire from spring balance and it registers a weight of 7N in air. When the brass is lowered into fresh water until submerged. The balance shows a weight of 6.17 N. Find the relative density of brass object.

8.433

252

The position of an object moving along x-axis is given by x=3t+4t^2 where (t) is in seconds. Calculate the velocity of the object at t=0 seconds referred to as v(0).

3 m/s

253

The position of an object moving along x-axis is given by x=3t+4t^2 where (t) is in seconds. Calculate the velocity of the object at t=2 seconds referred to as v(2) .

19 m/s

254

A box slides down an incline with uniform acceleration. It starts from rest and gains a speed of 4.8 m/s in 6 seconds. Find acceleration at the end of 4 seconds.

0.8 m/sq.s

255

A box slides down an incline with uniform acceleration. It starts from rest and gains a speed of 4.8 m/s in 6 seconds. Find the distance covered in 4 seconds.

6.4 m

256

Certain force acting on a mass 12 kg causes a particular acceleration. When the same force is applied on a body of mass 'x' kg, the acceleration produced = 4 m/sq.s. the total acceleration produced when th force acts on the two bodies tied together is 2.72 m/sq.s. Calculate 'x'

25.5 kg

257

Calculate the resultant force ( magnitude and angle) to replace two forces P= 60 N and Q=90 N making an angle of 20 deg between them. Assume P along X-axis

147.81 N, 12.019 deg.

258

A car starts from rest and attains an acceleration of 12 m/sq.s in 14 seconds. Calculate the distance travelled by car during this time.

1176 m

259

Mass of 5.4 kg is suspended from a spring with a spring constant of 19.6 N/mm. Find the elongation of spring. Take g= 9.81 m/sq.s

2.703 mm

260

Bus is moving with a uniform speed of 1.2 m/s. A man 6 m behind the bus runs with a speed of 4.2 m/s. How long does the man take to catch the bus?

2 s

261

What is the angular velocity of an object rotating at speed of 5 rotations/s and hanging from a string of length of 4 m

31.42 rad/s

262

A ball falls freely from rest. Find the distance of fall after 5 seconds. Take g=10 m/sq.s

125 m

263

A ball falls freely from rest. Find the speed at 60 m from point of fall. Take g=10 m/sq.s

34.64 m/s

264

Two boys start running straight towards each other from two points that are 100 m apart. One runs with speed of 10 m/s and the other runs with 15 m/s. How close is their meeting point to the starting point of the first boy?

40 m

265

A train running at 40 m/s uniformly stops after 24 s. Find deceleration.

1.6 m/sq.s

266

A train running at 40 m/s uniformly stops after 24 s. Find the distance travelled.

480 m

267

A ball is thrown vertically up with a velocity of 45 m/s from top of tower having height 50 m. Finally, it falls down. Calculate the time (t) that elapses from the instant that the ball was thrown until it passes the edge of the tower on its way down. Take g = 10 m/sq.s

9 s

268

A ball is thrown vertically up with a velocity of 45 m/s from top of tower having height 50 m. Finally, it falls down. Calculate the velocity of the ball when it hits the ground.Take g = 10 m/sq.s

55 m/s

269

Mass of cubical box is 5 kg and the dimensions are 30 cm x 30 cm x 30 cm. If the weight of the container is 1000 kg, calculate the weight of the container of size 4.5 m x 6 m x 3 m filled with these boxes.

16000 kg

270

An iron ball of mass 150 kg is lifted by a pulley through height of 16.2 m in 18.2 seconds. Efficiency of pulley is 75%. Calculate the energy consumed in lifting the ball. Take g= 9.81 m/sq.s

31.784 kJ

271

A ball is dropped from the elevator moving up with uniform velocity of 15 m/s. If the ball reaches the ground in 12 seconds, calculate the height of elevator when ball was dropped . Take g = 10 m/sq.s

540 m

272

A ball is dropped from the elevator moving down with uniform velocity of 15 m/s. If the ball reaches the ground in 12 seconds, calculate the height of elevator when ball was dropped . Take g = 10 m/sq.s

900 m

273

A locomotive pulls a train with a uniform velocity of 72 kmph and exerts a tractive force of 15 kN. Find the work done by the locomotive in 90 minutes.

1620 MJ

274

Calculate the work done in pulling a block of wood 300 kg for length of 7m up a smooth inclined plane which makes 40 degrees with the horizontal. Take g= 9.81 m/sq.s

13.242 kJ

275

At a certain instance a body of mass 10 kg falling freely under the force of gravity was found to be falling at 20 m/s. What force will stop the body in 2 seconds? Take g=9.81 m/sq.s

198.1 N

276

At a certain instance a body of mass 10 kg falling freely under the force of gravity was found to be falling at 20 m/s. What force will stop the body in 2 minutes? Take g=9.81 m/sq.s

99.767 N

277

A wooden block with mass m=3 kg is lying on a horizontal table. It is hit by a bullet with mass m=5 gm. The bullet remains in the block after colliding with it. The block moves on the table a distance of 25 cm. The coefficient of kinetic friction (µk)= 0.2. Find starting speed of bullet. Take g=9.81 m/sq.s

595.29 m/s

278

A pile of wood is hit with a free falling hammer at a speed of 12 m/s. By neglecting the frictional force, calculate the height from which the hammer started to fall.

7.2 m

279

Find the least force to pull a body of weight 224 N up an incline of 15 deg. Take µ= 0.24.

106.87 N

280

A bullet of mass 0.04 kg travelling with velocity of 300 m/s strikes and gets embedded in a block of mass 0.36 kg. After the impact, the bullet and body moves a distance of 49 m. What is the coefficient of friction of rough surface . Take g=10 m/sq.s

0.918

MECH NOTES FOR CLASS 4 PART A

Have a great day ahead.