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 $\left(\frac{n}{n+1}\right)mgR$

Change in P.E.$=\frac{-GMm}{(n+1)R}-\left(\frac{-GMm}{R}\right)=\left(\frac{GMm}{(n+1)R}\right)(-1+(n+1\left)\right)$

$=\left(\frac{GMm}{R}\right)\frac{\left(n\right)}{n+1}$
But $g=GM/R^2$ or $GM=g{R}^2$
Putting this value, we get Change in P.E. $=mgR\left(\frac{n}{n+1}\right)$