Question

If $g$ is the acceleration due to gravity on earth's surface, the gain in potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is:

• A. $\left(1/4\right)mgR$
• B. $mgR$
• C. $2mgR$
• D. $\left(1/2\right)mgR$

Answer 1

The correct option is D $\left(1/2\right)mgR$

Potential energy on the surface of earth $P_E=\frac{-GMm}{R}$

Potential energy of height $R$ from the surface of earth $P_{\left(R\right)}=\frac{-GMm}{2R}$

Gain in potential energy $P_G=\frac{-GMm}{2R}-\left(\frac{-GMm}{R}\right)=\frac{GMm}{2R}$

Also,

$g=\frac{GM}{R^2}$

On putting the value of $\frac{GM}{R}$ in above expression we get, $P_G=\frac{mgR}{2}$