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  4. A mass m is raised from a distance 2R from the surface of the earth to 3R . Work done to do so against gravity will -

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Q. A mass $m$ is raised from a distance $2R$ from the surface of the earth to $3R$ . Work done to do so against gravity will -

NTA AbhyasNTA Abhyas 2022

Solution:

Solution

$U_{i}=- \, \frac{G M m}{\left(2 R + R\right)}$
$U_{f}=- \, \frac{G M m}{\left(R + 3 R\right)}$
$W=\Delta U=U_{f}- \, U_{f}$
$=\frac{G M m}{12 R}=\frac{G M}{R^{2}} \, \times \, \frac{m R}{12}$
$=mgR/12$