Doubt from Gravitation

#1

From a uniform solid sphere of radius R , a sphere of radius R/2 is removed and taken to infinity . The work required by external agent to achieve this is ? Take original mass as M . Tanmay Sir , Pratyaksh Sir pls.help

#2

Anyone ?? Tanmay sir , Ayan sir ,Sneha ..

#3

This one too Tanmay Sir .

#4

Work done is change in Potential energy of system, final PE =0 and initially it was self energy of the uniform solid sphere that is
W = \frac{-3GM^2}{5R}

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#5

How final PE=0?
Only the interaction energy between the two will be zero, but still the self energy of sphere with cavity and a sphere of radius R/2 exists.
@pratyaksh_2019 please correct me if I'm wrong.

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#6

#7

Anyone ?? Pls solve

#8

Pratyaksh sir , Tanmay Sir

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#11

Pls check the answer i have tried to solve.Tanmay

#12

Sir sry but answer is wrong

#13