Doubt from Gravitation

gravitation
work-done
moderate
unsolved
pp
#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}

1 Like
#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.

2 Likes
#6

yeah my bad

#7

Anyone ?? Pls solve

#8

Pratyaksh sir , Tanmay Sir

#9

#10

#11

Pls check the answer i have tried to solve.Tanmay

#12

Sir sry but answer is wrong

#13

Can any student ask their coaching teachers about this problem ??

#14

centre of mass of big sphere got changed due to carving out of
Sphere of radius R/2 so distance between two sphere shouldnot be R/2 it got changed.
So let me try to incorporate it in the problem and the lower limit of intregation should be changed. Ok let me try

#15

#16

Tanmay Sir sry this one is too wrong , actually question was this :

answer given is 5 , pls help.others Ayan sir , Sonu , Samarth , Sneha