TRIVIA TUESDAY

Question-10 : A smooth Land.....

Suppose your mass is 60 kg and you are standing on a tree branch that is at a height of 15 m from the ground. To land softly, you’ll have to bend your legs, such that your center of mass descends by ∆h. What is the minimum value of ∆h so that you can land safely without breaking your tibia. Here, Take g = 10 m/s^2 , Cross Section of tibia ≈ 3.2 cm^2 , Max compressing force required to break the tibia in lower leg ≈ 1.6 × 10^8 N/m^2

Date: 25-01-2022

Deadline: 10A.M (IST), 30-01-2022

Question-9 : Is Magnetic field strong ?

A group of scientists are working on estimating the magnetic field of the newly discovered inhabitable solar system. The system of two planets charged with equal charges of Q = 100 TC and with equal masses of M = 5 · 10^24 kg orbiting each other at a distance of d = 500 000 km apart. determine the magnitude of a magnetic field that is present at the center of mass of the two-planet system. (Assume two planets as point charges and assume that their orbits are circular)

Date: 18-01-2022

Deadline: 10A.M (IST), 23-01-2022

Question-8 : Ice is melting!!

There was a block of ice in an isolated container at temperature 0° C. We wanted to determine its mass, therefore we let some steam with a temperature of 100° C into the container, but we could not determine the exact amount or the steam. After re-closing the container all the ice melted, and the equilibrium temperature become 10° C. Then, once more we let some steam of temperature 100° C into the container, but again we could not determine its exact amount. The temperature in the container became 15° C. Finally, we let again some steam into the container, and this time we could determine it's mass, which was 0.3kg. The new equilibrium temperature in the container becomes 23° C. Determine the mass of the ice block.

Date: 11-01-2022

Deadline: 10A.M (IST), 16-01-2022

Question-7 : Salman goes green!!

Salman is watering his garden. He took a cylindrical bucket with base area S=420 cm^2 and filled it with water up to a height h= 40 cm. Afterwards, he made a hole with area s= 2 cm^2 in the bottom base and started watering. What's the longest row of plants which he's able to water, if his speed is u= 1m/s? (Hint The speed with which water flows out of the hole is given by the formula v = μs√2gx with a coefficient μ= 0.6 where x is the current water level height.).

Date: 04-01-2022

Deadline: 10A.M (IST), 09-01-2022

Question-6 : An Asteroid Tragedy!!

While on your space mission, you encounter a swarm of asteroids and crash land on an exoplanet. Luckily your shuttle has an emergency escape capsule and some fuel left. In order to plan your escape you need to know the escape velocity of the planet you are stranded on. You have a weighing machine, a shovel and a filled water container of 1 litre. You know your weight to be "W" newtons on earth and exoplanet has a g' m/s^2 acceleration due to gravity. Assume that the density of the exoplanet is constant. Using the above data and the items in hand, calculate the escape velocity.

Date: 28-12-2021

Deadline: 10A.M (IST), 02-01-2022

Question-5 : Spider-Man No way reaches surface!!

Green Goblin who was chasing Spiderman (M = 50Kg), who was about to save MJ who slipped off a building. Spiderman notices that his web-shooters fail to work at that moment. Ned immediately finds out that Spiderman's body has a charge of 10 C and also notices a homogeneous magnetic field of 10T below the building reaching a height w=10 meters and he also says that Spiderman need not worry as he will not reach the surface and informs this to him. The field is perpendicular to the vertical, the velocity of Spiderman at the moment of entering the magnetic field has a vertical component only. Assume that the magnetic field is pointing in the right direction so Spiderman does not hit the building. (Neglect air resistance and acceleration due to gravity is g = 9.8 m/s^2). What is the maximum height of the building h (in meters) from which Spiderman can jump without reaching the surface?

Date: 21-12-2021

Deadline: 10A.M (IST), 26-12-2021

Question-4 : Let's save Roy!!

Roy lands up in a planet in a parallel universe where Gravitational force is given by:

Question-3 : Tunnel in an Exoplanet!!

The exoplanet Kepler-138c has radius RK = 1.2 RE, where RE is the radius of the Earth, and density equal to that of the Earth. The inhabitants dug a tunnel straight through the centre of the planet (along the diameter). How much longer will it take to free-fall through this tunnel (without friction or propulsion) than through a similar tunnel on Earth? Give your answer in seconds. Assume that both planets are homogeneous.

Date: 07-12-2021

Deadline: 10A.M (IST), 12-12-2021

Question-2 : Asteroid is a conductor!!

Shelly, an Astronomer and Bert, a Geologist when examining the asteroid chunk decides to calculate the resistivity of chunk (ρ) to decide its metallic composition. They find out it has resistance of ’Φ’. Help them find expression for resistivity of chunk in terms of a, b, h and . Assume the material to behave like good conductor.

Just for Fun: Do checkout what happens to Resistance and Resistivity if current flows radially.

Date: 30-11-2021

Deadline: 10A.M (IST), 05-12-2021

Question- 1 : Which ball reaches first ?

A tube in the shape of a rectangle with rounded corners is placed in a vertical plane as shown. Two ball bearings are introduced simultaneously at the upper right-hand corner. One travels by path AB while other by path CD. Which will arrive first at lower left-hand corner?

Date: 23-11-2021

Deadline: 10A.M (IST), 28-11-2021