Question

The particles $A$ and $B$ of mass $m$ each are separated by a distance $r$. Another particle $C$ of mass $M$ is placed at the midpoint of $A$ and $B$. Find the work done in taking $C$ to a point equidistant $r$ from $A$ and $B$ without acceleration ( $G=$ Gravitational constant and only gravitational interaction between $A,B$ and $C$ is considered)

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

Answer 1

Answer: (B)

Since particle $C$ is moved without any acceleration,
$\Rightarrow \Delta K.E=0$
$\Rightarrow$ Work done by external agent $+W_{\text{gravitation }}=0$
$\Rightarrow$ Work done by external agent $=-Wg$
$=-(-\Delta U)$
$=\Delta U$
$=U_t-U_{\text{in }}$
$U_f=-\frac{GMm}{r/2}-\frac{GMm}{r}=-\frac{2GMm}{r}$
$U_i=-\frac{GMm}{r/2}-\frac{GMm}{r/2}=-\frac{4GMm}{r}$
$\Rightarrow$ Work done $=\frac{2GMm}{r}$