Question

A body of mass m is moved to a height equal to the radius of the earth $R$. The increase in its potential energy is:

• A. $\frac{GMm}{R}$
• B. $2\frac{GMm}{R}$
• C. $\frac{1}{2}\frac{GMm}{R}$
• D. $\frac{1}{4}\frac{GMm}{R}$

Answer 1

The correct option is C $\frac{1}{2}\frac{GMm}{R}$

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 $R$ above the surface of earth. Potential energy is given by,
$U_f=-\frac{GMm}{R+R}=-\frac{GMm}{2R}$

Now, change in potential energy,
$\Delta U=U_f-U_i$
or, $\Delta U=-\frac{GMm}{2R}+\frac{GMm}{R}$
or, $\Delta U=\frac{1}{2}\frac{GMm}{R}$