## Question

A body of mass *m* is moved from the surface of the earth to a height *h *(*h*is not negligible in comparison to radius of earth *R _{e}*). Prove that the increase in potential energy is

### Solution

Let *M _{e}* be the mass of the earth and

*R*its radius. Then the gravitational potential energies of a body of mass

_{e}*m*on the earth’s surface, and at a height

*h*from earth’s surface are

∴ Increase in potential energy of the body is

#### SIMILAR QUESTIONS

Calculate that imaginary angular velocity of the earth for which effective acceleration due to gravity at the equator becomes zero. In this condition what will be the length (in hours) of the day?

(*R _{e}* = 6400 km,

*g*= 10 ms

^{–2})

Determine the speed with which the earth would have to rotate on its axis so that a person on the equator would weigh 3/5 th as much as at present. Take the equatorial radius as 6400 km.

At what height above the earth’s surface the acceleration due to gravity will be 1/9 th of its value at the earth’s surface? Radius of earth is 6400 km.

The radius of the earth is approximately 6000 km. What will be your weight at 6000 km above the surface of the earth? At 12000 km above? At 18000 km above?

Calculate the gravitational field strength and the gravitational potential at the surface of the moon. The mass of the moon is kg and its radius is

.

The intensity of gravitational field at a point situated at earth’s surface is 2.5 N/kg. Calculate the gravitational potential at that point. Given: radius of earth, .

At a point above the surface of the earth, the gravitational potential is and the acceleration due to gravity is 6.4 ms^{–2}. Assuming the mean radius of the earth to be 6400 km, calculate the height of this point above the earth’s surface. ^{ }

The mass of the earth is and its radius is m. How much work will be done in taking a 10-kg body from the surface of the earth to infinity? What will be the gravitational potential energy of the body on the earth’s surface? If this body falls from infinity to the earth, what will be its velocity when striking the earth?

The radius of earth is 6400 km and mass is kg. What will be the gravitational potential energy of a body of 200 kg placed at a height of 600 km from the surface of the earth?

.

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is 0.5 *R _{e}*, where

*R*is radius of earth. The mass of earth is

_{e}*M*.

_{e}