Question

Assuming the radius of the earth as $R$, the change in gravitational potential energy of a body of mass $m$, where it is taken from the earth's surface to a height $3R$ above its surface is

• A. $\frac{2}{3}\frac{GMm}{R}$
• B. $\frac{3}{4}\frac{GMm}{R}$
• C. $3\frac{GMm}{R}$
• D. $\frac{3}{2}\frac{GMm}{R}$

Answer 1

The correct option is B $\frac{3}{4}\frac{GMm}{R}$

When the object is placed at surface of Earth, potential energy is given as,
$U_i=-\frac{GMm}{R}$
where $m$ is mass of the object, $M$ is mass of the earth and $R$ is the radius of the earth.

when the object is placed at height $3R$ above the surface of earth. Potential energy is given by,
$U_f=-\frac{GMm}{R+3R}=-\frac{GMm}{4R}$

Now, change in potential energy,
$\Delta U=U_f-U_i$
or, $\Delta U=-\frac{GMm}{4R}+\frac{GMm}{R}$
or, $\Delta U=\frac{3}{4}\frac{GMm}{R}$