Question

Potential at the centre of uniform solid sphere of mass
Mand radius R is given by​

Answer 1

Answer:

Gravitational potential at any inside point is given as  

V=−  

2R  

3

 

GM

​  

(3R  

2

−r  

2

)....(i)

for r=  

2

R

​  

V=−  

8R

11GM

​  

 

Subtracting potential due to cavity of mass M  

c

​  

=  

8

M

​  

 and R  

c

​  

=  

2

R

​  

 

Gravitational potential at center is obtained by substituting r=0 in equation (i) =−  

2R  

c

​  

 

3GM  

c

​  

 

​  

 

V=−  

8R

11GM

​  

−(−  

2R  

c

​  

 

3GM  

c

​  

 

​  

)=−  

8R

11GM

​  

+  

2  

2

R

​  

 

3G  

8

M

​  

 

​  

 

⇒V=−  

R

GM

​

Explanation: