Question

23. Calculate the final speed of an object dropped on Earth from altitude of 8 times the radius of Earth. (hint: neglect friction

    due to atmosphere and use expression of gravitational potential energy and principle of conservation energy. Answer =

    10.6 km/s).

Answer 1

The gravitational potential energy at a point is defined as the workdone to move a body from infinity to that point and if a body is falling towards earth the gravitational potential energy of the body at a distance r from the earth surface is given by,

Where

M= mass of earth=

m=mass of the body.

So if the body is falling from a hight to a hight the change in gravitational potential energy is given by

If the velocity of the body is , the change in kinetic energy from velocity 0 to is given by

According to conservation of energy,

For earth surface radius of earth is

Here