Question

$X$ and $Y$ are two points at respective distances $R$ and $2 R$ from the centre of Earth, where $R$ is greater than the radius of Earth. The gravitational potential at $X$ is $-800$ $kJ kg ^{-1}$. When a $1 kg$ mass is taken from $X$ to $Y$, the work done on the mass is

• A. 400 kJ
• B. 200 kJ
• C. -200 kJ
• D. 80 kJ

Answer 1

Answer: (A)

$ V_{Y}-V_{X}=\left[\frac{-G M}{(2 R)}\right]-\left[\frac{-G M}{R}\right]$
$ \Rightarrow \Delta V=\frac{G M}{2 R}$
Here, $\,\, V_{X}=-\left(\frac{G M}{R}\right)=-800 kJ kg ^{-1}$
$\Rightarrow \Delta V=\frac{800}{2}=400 kJ / kg$
$W_{ ex }=m \Delta V=(1 kg )\left(400 kJ kg ^{-1}\right)=400 kJ$