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Gravitation Part 1

Section: Physics

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Question : 89 of 100

Marks: +1, -0

A particle of mass

10\,\text{g}

is kept on the surface of a uniform sphere of mass

100\,\text{kg}

10\,\text{cm}

. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take

G=6.67 \times 10^{-11}\,\text{Nm}^2/\text{kg}^2

$3.33 \times 10^{-10}\,\text{J}$
$13.34 \times 10^{-10}\,\text{J}$
$6.67 \times 10^{-10}\,\text{J}$
$6.67 \times 10^{-9}\,\text{J}$

Solution:

We know, Work done = Difference in potential energy

\;\therefore\ W=\Delta U=U_f-U_i=0-\left[ -\frac{G M m}{R} \right]

\;\Rightarrow W=\frac{6.67 \times 10^{-11} \times 100}{0.1} \times \frac{10}{1000}

\;=6.67 \times 10^{-10}\,\text{J}

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