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  4. Let the minimum external work done in shifting a particle from centre of earth to earth’s surface be W1 and that from surface of earth to infinity be W2. Then (W1/W2) is equal to

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Q. Let the minimum external work done in shifting a particle from centre of earth to earth’s surface be $W_1$ and that from surface of earth to infinity be $W_2$. Then $\frac{W_1}{W_2}$ is equal to

Gravitation

Solution:

$\frac{W_{1}}{W_{2}} = \frac{-\frac{GM}{R} -\left(-\frac{3}{2} \frac{GM}{R}\right)}{0 - \left(- \frac{GM}{R}\right)} = \frac{1}{2}$