Question

When a mass $2\text{kg}$ is shifted from infinity to a point in gravitational field, it is found that work done by external force is $-100\text{J}$. If the mass is doubled and taken again from the same point to infinity without accelerating it, then the work done by gravitational force will be

• A. $-100\text{J}$
• B. $-200\text{J}$
• C. $200\text{J}$
• D. $400\text{J}$

Answer 1

The correct option is B $-200\text{J}$

Work done by external force in taking mass $m$ from infinity to a point $\text{P}$ is related to the gravitational field as ,

$$\frac{W_{\text{ext}}(\infty \to P)}{m}=V_P-V_{\infty }$$As, $V_{\infty }=0$

$\Rightarrow \frac{W_{\text{ext}}(\infty \to P)}{m}=V_P-0=V_P$

$\Rightarrow W_{\text{ext}}(\infty \to P)=m{V}_P$

Thus, gravitational potential at point $P$ is

$V_P=\frac{W_{\text{ext}}(\infty \to P)}{m}=\frac{-100}{2}=-50\text{J/kg}$

If mass is doubled and taken from $P$ to $\infty$,

$W_{\text{ext}}(P\to \infty )=-(4\times -50)\text{J/kg}=200\text{J}$

Therefore, work done by gravitational force,

$W_{\text{g}}(P\to \infty )=-W_{\text{ext}}(P\to \infty )=-200\text{J}$

Hence, option (b) is correct answer.