Gravitational Potential Energy

Q. A body of mass m is placed on earth surface is taken to a height of h = 3R, then change in gravitational potential energy is

1. $\frac{mgR}{4}$
2. $\frac{2mgR}{3}$
3. $\frac{3mgR}{4}$
4. $\frac{mgR}{4}$

Q.

How do we use gravitational energy in everyday life?

Q.

Water falls from a height of 100 m. Calculate the rise in temperature of water when it strikes the bottom. Given, S${}_w$​ = 4200 Jkg${}^{-1}$​${}^0$​C${}^{-1}$​ and g = 10 m/s${}^2$​.

1. 0.273°C

2. 0.360°C

3. 0.238°C

4. 1.258°C

Q. The gravitational potential energy above the surface of earth is .

1. mgh
2. zero
3. $\frac{GM}{R^2}$

Q. In a system of units energy E, density d, and power P, are taken as fundamental units then the dimensional formula of universal gravitational constant G, will be

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.

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5}$$\frac{G{M}^2}{R}$ where x is __________. (Round off to the Nearest Integer). (M is the mass of the earth, R is the radius of the earth, and G is the gravitational constant)

Q.

A body of mass m rises to height$h=\frac{R}{5}$from the earths surface, where R is the earths radius. If g is the acceleration due to gravity at the earths surface, the increase in potential energy is

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.

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.

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.

A body of mass is placed on the earth s surface. It is taken from the earth s surface to a height $h=3R$, R is the radius of earth. The change in gravitational potential energy of the body is

Q.

1. $12.3kW$
2. $7.0kW$
3. $10.2kW$
4. $8.1kW$

Q. 15. Three point masses each of mass m are placed at the vertices of an equilateral triangle of side a. The gravitational potential due to these masses at the centroid of the triangle is??

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.

A rocket is launched vertically from the surface of the earth of radius R with an initial speed v. If atmospheric resistance is neglected, the maximum height attained by the rocket is given by

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. An object is taken to height 2R above the surface of earth , the increase in potential energy is

1. $\frac{mgR}{2}$
2. $\frac{mgR}{3}$
3. $\frac{2mgR}{3}$
4. 2 mgR

Q.

Define gravitational potential energy.

Q.

What is gravitational potential energy?

Q.

Two bodies of equal weight are kept at heights of h and 1.5 h, respectively. The ratio of their P. E. is:

1. 3:2

2. 2:3

3. 1:1

4. 4:3

Q. Which of the following physical quantity of a planet that revolves around Sun in an elliptical orbit is constant?

1. Angular momentum
2. Kinetic energy
3. Potential energy
4. Linear velocity

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

1. False
2. True

Q. two balls of masses 3m and m are seperated by distance l.find the position of centre of mass

Q. Two concentric spherical shells have masses M₁, M₂ and radii R₁, R₂ (R₁ < R₂). What is the force exerted by this system on a particle of mass m₁ if it is placed at a distance (R₁ + R₂)/2 from the centre?