CGPET 2016 Solved Paper

It is given, V=0 at r=∞
Gravitational potential at internal point of a solid sphere at a distance r, is given by the following formula
V=−

GM

R

[

3

2

−

r2

2R2

]
Here,
r=

R

2

V1=−

GM

R

[

3

2

−

R2

8R2

]
=−

GM

R

[

12−1

8

]
=−

11

8

GM

R

Because of sphere removed-
V2=

3

2

.

GM 8

R 2

=

3

2

×

2‌GM

8R

3

8

GM

R

The net potential at the center of the cavity
V=V1+V2
=−

11

8

GM

R

+

3

8

GM

R

=

GM

R

[

3

8

−

11

8

]
−

GM

R