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Question

# A planet of mass M has uniform density in a spherical volume of radius R. Calculate the work done by the external agent to deassemble the planet in eight identical spherical part against gravitational pull amongst its constitute particle.

A
920Gm2R.
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B
1920Gm2R.
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C
2020Gm2R.
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D
2120Gm2R.
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Solution

## The correct option is A 920Gm2R.self energy of Big sphere =−35GM2R43πR3=8×43πr3⇒r=R2 ⇒ Self energy of small sphere =−35×4×M264×R2=−35×GM232R⇒U=−35GM2R+8×35×GM232R=34×35GM2R ⇒U=920GM2RTherefor option A is correct.

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