Solutions: Physics Paper 2 IITJEE 2008 (IITJEE 2008)

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Solutions: Physics Paper 2 IITJEE 2008

1. A radioactive sample S1 having an activity of 5 Ci has twice the number of nuclei as another sample S2 which has an activity of 10 Ci. The half lives of S1 and S2

can be

(A) 20 years and 5 years, respectively

(B) 20 years and 10 years, respectively

(D) 5 years each

Ans

2. Consider a system of three charges

placed at points A, B and C respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60^o

Figure :

(A) The electric field at point O is directed along the negative x-axis

(B) The potential energy of the system is Zero

(D) The potential at point O is

Ans

3. A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10

cm. At a particular time t, the snap-shot of wave is shown in figure. The velocity of point P when its displacement is 5 cm is

Figure :

Ans.

Hence +ve y education

4. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is d/3 initially. Suppose

the liquid level decreases at a constant speed V, the time constant as a function of time t is

Figure :

Ans

The two capricious can be considered in series

5. A vibrating string of certain length L under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75

cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the

string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in

Hz is

Figure:

(A) 344 (B) 336 (C) 117.3 (D) 109.3

Ans

6. A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III, and IV are

respectively. The angle of incidence q for which the beam just misses entering Region IV is

Figure :

Ans

7. A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k, respectively (see figure I). The other ends are attached to

identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced

towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are

measured with respect to the equilibrium position of the block B. The ratio y/x is

Figure :

Ans

By conservation of energy

Note supports A/1 & A/2 are mailers and do not allow stretching S₁ does not expand when S₂ contracts.

8. A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,

Figure

(A) air from end 1 flows towards and 2. No change in the volume of the soap bubbles

(B) air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases

(D) air from end 2 flows toward end 1. Volume of the soap bubble at end 1 increases

Ans

r₂ > r₁ P₀ : atmospheric pressure

\P₂ < P₁

Air from 1 goes to 2

And since volume is constant volume from 1 goes to 2

9. A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle

which the speed of the bob is half of that at A, satisfies

Figure :

Ans.

By conservation of energy

Since the v_o is just sufficient

10. STATEMENT-1

For practical purposes, the earth is used as a reference at zero potential in electrical circuits.

and

STATEMENT-2

The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

(D) STATEMENT-1 is False, STATEMENT-2 is True

Ans

Statement 1 is true since earth is used as a reference at zero potential to measure potential difference which is independent of the reference

Statement 2 is true since the electric potential of a spherical shell is But statement 2 sloes not explanation statement 1

11. STATEMENT-1

The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.

and

STATEMENT-2

Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

(D) STATEMENT-1 is False, STATEMENT-2 is True

Ans

Statement 1 is true since the sensitivity of the moving will galvanometer increases by placing magnetic material.

Statement 2 there is ambiguity & zero cases wises

Case 1: cannot be early permanently migrated / demagnetized soft iron has magnetic permeability and can not be easily permanently magnetized . Hence it is the corrupt explanation of statement 1. Answer is a

Case 2: can not be easily magnetized / demagnetized during galvanometers operation. They are it does not act as a good electro magnet which is false. Answer is C

12. STATEMENT-1

For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

and

STATEMENT-2

If the observer and the object are moving at velocities V₁ and V₂ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is V₂ - V₁ .

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

(D) STATEMENT-1 is False, STATEMENT-2 is True

Ans

Statement 1 is true since when we obscure from a train we all comparing the angular velocity which is more for nearer objects

Statement 1 is true by definition of relative velocity

But it is wrong explanation of statement 2

13. STATEMENT-1

It is easier to pull a heavy object than to push it on a level ground.

and

STATEMENT-2

The magnitude of frictional force depends on the nature of the two surface in contact.

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

(D) STATEMENT-1 is False, STATEMENT-2 is True

Ans.

Statement 1 is true (by observation & explained also)

Since N > N¹ => f > f¹ => it is easier to pull than to push

Statement 2 is also true but it is not the correct explanation.

Paragraph for the question No. 14 - 16

The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density (r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

Figure :

14. The electric field at r = R is

(A) independent of a (B) directly proportional to a

Ans.

The electric field at r = R depends on total nuclear change inside r £ R which is correct irrespective of P

15. For a = 0, the value of d (maximum value of asr shown in the figure) is

Ans.

16. The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

Ans.

We know that for a uniformly charged sphere

Hence we can conclude a = R for r to be cones.

Paragraph for the question No. 17 - 19

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the

figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and

the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a

distance L from the wall. The disk rolls without slipping with velocity . The coefficient of friction is m .

Figure :

17. The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is

Ans.

By Newton’s law:

2Kx - f = ma (1)

18. The centre of mass of the disk undergoes simple harmonic motion with angular frequency w equal to

Ans.

19. The maximum value of V₀ for which the disk will roll without slipping is

Ans.

By conversation of energy

20. Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 X 4 matrix given in the ORS.

Ans.

(i) Potential energy of simple Pendulum (displacement from mean position)²

Both p and s can be correct depending on the displacement of mean position

(ii) Displacement t² (for constant 0)

t (for a = 0)

At t = 0, displacement may be nor-zero

q, r, s are correct.

21. Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 X 4 matrix given in the ORS.

Ans.

(i) The process is adiabatic TV^v^-¹ = const.

=> V increase & T decrease

p is correct

(ii) PV² = const.

VT = const since PV² = const

v increases => T decreases

As T decreases & C is + ve

=> Gas loses heat

P, r are correct

=> TV^1/3 = const

=> s is correct

(D)

P₂ V₂ > P₁ V₁ (from figure)

=> T₂ > T₁ since PV/T = const

\ q is correct

Work Dons = Area under the graph ³ O

=> Q>O

Hence s i\s correct.=> s is correct

22. An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 X 4 matrix given in the ORS. .