Question

If $W_1$ work is done against gravitational attraction to carry $10$ kg mass from earth's surface to infinity, then the magnitude of work done by the gravitational attraction in bringing $20$ kg mass from infinity to the centre of earth is

• A. $2W_1$
• B. $3W_1$
• C. $\frac{W_1}{2}$
• D. $4W_1$

Answer 1

The correct option is

B

3W13W_13W1​

$potentialduetosolidsphere$

$v=\frac{Gm\{3R^2-r^2\}}{2R^3};atcenterr=0$

$\therefore v=-\frac{\frac{3}{2}Gm}{R}$

$W_2=20(V_i-V_f)$

$=20\{0-(-\frac{3}{2}G\frac{m}{R})\}$

GM(10) R=w1⇒32GM(20) R=3w1$$\begin{array}{c}\frac{GM\left(10\right)}{R}=w_1\\ \Rightarrow \frac{3}{2}\frac{GM\left(20\right)}{R}=3w_1\end{array}$$RGM(10) ​=w1​⇒23​RGM(20) ​=3w1​​

$\therefore$ Option $B$ is correct.