21.

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius R around the sun will be proportional to

• 
• 

• Rⁿ

• Rⁿ

A comet orbits around the Sun in an elliptical orbit. Which of the following quantities remains constant during the course of its motion ?

• Linear velocity

• Angular velocity

• Angular momentum

• Kinetic energy

Consider a satellite moving in a circular orbit around Earth. If K and V denote its kinetic energy and potential energy respectively, then (Choose the convention, where V = 0 as r → ∞)

• K = V

• K = 2V

• V = − 2K

• K = − 2V

Assuming the mass of Earth to be ten times the mass of Mars, its radius to be twice the radius of Mars and the acceleration due to gravity on the surface of Earth is 10 m/s². Then the acceleration due to gravity on the surface of Mars is given by

• 0.2 m/s²

• 0.4 m/s²

• 2 m/s²

• 4 m/s²

The semi-major axis of the orbit of Saturn is approximately nine times that of Earth. The time period of revolution of Saturn is approximately equal to

• 81 years

• 27 years

• 729 years

• $\sqrt[3]{81} \mathrm{years}$

A body hanging from a massless spring stretches it by 3 cm on Earth's surface. At a place 800 km above the Earth's surface, the same body will stretch the spring by (Radius of Earth = 6400 km)

• $\left(\frac{34}{27}\right) \mathrm{cm}$

• $\left(\frac{64}{27}\right) \mathrm{cm}$

• $\left(\frac{27}{64}\right) \mathrm{cm}$

• $\left(\frac{27}{34}\right) \mathrm{cm}$

The acceleration due to gravity on the surface of a planet is one-fourth of the value on Earth. When a brass ball is brought to this planet, its

• mass is halved

• weight is halved

• mass becomes one-fourth

• weight becomes one-fourth

Polar satellites

• are high altitude satellite

• are widely used for telecommunication

• are used for environmental studies

• go around the Earth in a East-West direction

Angular momentum of the Earth revolving around the Sun in a circular orbit of radius R is proportional to

• $\sqrt{\mathrm{R}}$

• R

• R²

• R^1/3

A body of mass m is released from a height equal to the radius R of the Earth. The velocity with which it will strike the Earth's surface is

• $\sqrt{2\mathrm{gR}}$

• $\sqrt{\mathrm{gR}}$

• $\sqrt{2 \mathrm{mgR}}$

• $\sqrt{\mathrm{mgR}}$