Question

The change in potential energy when a body of
mass m is raised to height nR from the earth's
surface is (R is radius of earth)​

Answer 1

Answer:

Here is your answer.....

Answer 2

Answer:

Given:

An object is taken to a height nR from earth surface

To find:

Change in Potential energy of the object.

Diagram:

Please refer to the attached photo to understand better.

Formulas used:

Potential at any point wrt centre of Earth

= - (GMm)/r ,

where "r" is distance from centre of Earth.

Calculation:

First look at the diagram.

Potential at Earth surface

= - GMm/R .........(i) [R - Radius of Earth]

Potential at a height nR

= - GMm/(nR + R)

= - GMm/{(n+1)R} ..........(ii)

Change in Potential Energy

= (ii) - (i)

=[ - GMm/{(n+1)R} ] - [ - GMm/R]

= - GMm [ 1/(n+1) - 1]

= {n/(n+1) } GMm/R

= {n/(n+1) } [m (GM/R²) ×R]

= (n/n+1) mgR [ as GM/R² = g]

So final answer = (n/n+1) mgR.