Gravitational Potential Energy

Q.

The potential at the surface of a planet of mass M and radius R is assumed to be zero. Choose the most appropriate option

1. Both (a) and (b) are correct

2. 

3. 

4. Both (a) and (b) are wrong

Q. Gravitational potential of an object of mass m at a height h from the surface of earth, where h is comparable to the radius R of the earth is

1. $-\frac{GMm}{R+h}$
2. $\frac{GMm}{R+h}$
3. \N

Q. Gravitational potential energy is the energy possessed by an object due to its position.

1. False
2. True

Q.

A rocket is launched vertically from the surface of a planet with radius $R$. Rocket has an initial speed $v$. If atmospheric resistance is neglected, the maximum height attained by the rocket is given by________.
Take $g=\frac{GM}{R^2}$.

1. $h=\frac{R}{(\frac{2gR}{v^2}-1)}$

2. $h=\frac{R}{(\frac{2gR}{v^2}+1)}$

3. $h=R(\frac{2gR}{v^2}-1)$

4. $h=R(\frac{2gR}{v^2}+1)$

Q.

Escape velocity of a body on a planet is $100m{s}^{-1}$. What is the gravitational potential energy of the body at the surface, if the mass of the body is $1kg$?

1. - 2400 J

2. 5000 J

3. - 5000 J

4. - 1000 J

Q. Assuming the radius of the earth as $R$, the change in gravitational potential energy of a body of mass $m$, where it is taken from the earth's surface to a height $3R$ above its surface is

1. $\frac{2}{3}\frac{GMm}{R}$
2. $\frac{3}{4}\frac{GMm}{R}$
3. $3\frac{GMm}{R}$
4. $\frac{3}{2}\frac{GMm}{R}$

Q. A body of mass m is moved to a height equal to the radius of the earth $R$. The increase in its potential energy is:

1. $\frac{GMm}{R}$
2. $2\frac{GMm}{R}$
3. $\frac{1}{2}\frac{GMm}{R}$
4. $\frac{1}{4}\frac{GMm}{R}$

Q.

The gravitational potential energy of a body of mass m at the earths surface $-mg{R}_e$. Its gravitational potential energy at a height $R_e$ from the earths surface will be (Here $R_e$ is the radius of the earth)

1. 

2. 

3. 

4. 

Q.

A small body starts falling on to the earth from a distance equal to the radius of the earths orbit. How long will the body take to reach the sun? Express the time in terms of T, period of revolution of the earth round the sun

1. 

2. 

3. 

4. T

Q.

A body of mass m kg. starts falling from a point 2R above the earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the eart’s surface [R – Radius of earth, M – Mass of earth, G – Gravitational constant]

1. 

2. 

3. 

4.