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Q.

Two particles each of mass 1kg are separated by a distance of 1m in a gravitational field. The work done to increase the separation between them to 2m is

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a

G

b

2G

c

\frac{G}{4}

d

\frac{G}{2}

answer is B.

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Detailed Solution

m_{1} = 1 kg

m_{2} = 1 kg

r_{1} = 1 m

r_{2} = 2 m

$U_{1} = - G \frac{m_{1} m_{2}}{r_{1}}$

$= - G \times \frac{1 \times 1}{1} = - G$

$U_{2} = - G \frac{m_{1} m_{2}}{r_{2}}$

$= - G \times \frac{1 \times 1}{2} = - \frac{G}{2}$

$W = U_{2} - U_{1}$

$= - \frac{G}{2} + G = \frac{G}{2}$

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Two particles each of mass 1kg are separated by a distance of 1m in a gravitational field. The work done to increase the separation between them to 2m is