Question

A small body is initially at a distance $r$ from the centre of earth. $r$ is greater than the radius of the earth. If it takes $W$ joules of work to move the body from this position to another position at a distance $2r$ measured from the centre of earth, then how many joules would be required to move it from this position to a new position at a distance of $3r$ from the centre of the earth.

• A. $\frac{W}{5}$
• B. $\frac{W}{3}$
• C. $\frac{W}{2}$
• D. $\frac{W}{6}$

Answer 1

The correct option is B $\frac{W}{3}$

Work done to move the body in the gravitational field is equal to change in the potential energy of the body.
i.e.
$W=-\frac{GMm}{2r}-(-\frac{GMm}{r})$
$\Rightarrow W=\frac{GMm}{2r}$
Now when the body is moved from $2r$ to $3r$, change in PE is
$W^{\prime }=-\frac{GMm}{3r}-(-\frac{GMm}{2r})=\frac{1}{3}\frac{GMm}{2r}=\frac{W}{3}$