Question

A body of mass 'm' is raised from the surface of the earth to a height 'nR' (R- radius of earth). Magnitude of the change in the gravitational potential energy of the body is (g-acceleration due to gravity on the surface of earth)

• A. $\left(\frac{n}{n+1}\right)mgR$
• B. $\left(\frac{n-1}{n}\right)mgR$
• C. $\frac{mgR}{n}$
• D. $\frac{mgR}{(n-1)}$

Answer 1

The correct option is A $\left(\frac{n}{n+1}\right)mgR$

At surface gravitaional potential energy $U_1=-\frac{GMm}{R}$

At height $nR,U_2=-\frac{GMm}{R+nR}$

$|U_2-U_1|=|\left(\frac{-GMm}{R+nR}\right)-\left(\frac{-GMm}{R}\right)|=\frac{GMm}{R}-\frac{GMm}{R+nR}\Rightarrow \frac{GMm}{R}[1-\frac{1}{n+1}]\Rightarrow \left(\frac{n}{n+1}\right)\frac{GMm}{R}\Rightarrow \left(\frac{n}{n+1}\right)mgR$