Question

A small body is at a distance $r$ from the centre of Mercury, where $r$ is greater than the radius of Mercury. The energy required to shift the body from $r$ to $2r$ measured from the centre is $E$. The energy required to shift it from $2r$ to$3r$ will be

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

Answer 1

The correct option is C $\frac{E}{3}$

$E=U_2-U_1$

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

$E^1=-\frac{GMm}{3R}+\frac{GMm}{2R}=\frac{GMm}{6R}$

$E^1=\frac{E}{3}$