IIT JEE Advanced 2010 Paper 1

The sine component of gravitational force from a mass element da at a distance 3R + dr and its counterpart at opposite end cancel each other. Thus, the total gravitational force at point p is the mass density σ, which is given as
σ =

M

2πR2(16−9)

=

M

14πR2

Now, V = -

4R

∫

3R

Gσ2πrdr

√r2+16R2

= −G2π‌

4R

∫

3R

rdr

√r2+16R2

V = Gσ2π|√r2+16R2|3R4R = Gσ2πR(4√2−5)
Substituting the value of σ, we get
V =

2GM

7R

(4√2−5)