Question

A body of mass $m$ is lifted from the surface of earth to a height equal to $R/3$,where $R$ is the radius of earth. Potential energy of the body increases by

• A. $\frac{mgR}{3}$
• B. $\frac{mgR}{4}$
• C. $\frac{mgR}{5}$
• D. $\frac{mgR}{9}$

Answer 1

The correct option is B $\frac{mgR}{4}$

The change in potential energy when a body is raised by a height $h$ from the surface of the Earth is given by

$\Delta U=\frac{mgh}{(1+h/R)}$

from question, $h=R/3$

$\Rightarrow \Delta U=\frac{mgR}{3}\times \frac{1}{[1+(R/3\left)/R\right]}=\frac{mgR}{4}$

Hence, option $\left(b\right)$ is the correct answer.

Why this question: Note - The change in potential energy when a mass $m$ is raised from the surface of the Earth to a height $h$ is given by $\Delta U=\frac{mgh}{(1+h/R)}$