Question

A body of mass $m$ is taken from the earth's surface to the height equal to twice the radius $R$ of the earth. The change in potential energy of the body will be -

• A. $\frac{1}{3}mgR$
• B. $2mgR$
• C. $\frac{2}{3}mgR$
• D. $3mgR$

Answer 1

The correct option is C $\frac{2}{3}mgR$

The gravitational potential energy at a point, on or above the earth's surface, is given by,

$U=-\frac{GMm}{r}$
Here, $r$ is the distance of the mass $m$ from the centre of earth.

$\Rightarrow \Delta U=U_f-U_i$

$=-\frac{GMm}{R+2R}-(-\frac{GMm}{R})$

$=\frac{GMm}{R}(1-\frac{1}{3})$

$=\frac{2}{3}mgR$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.