CGPET 2018 Solved Paper

According to question,Let gravitational field is zero at point C.
∴I1=I2
⇒

Gm

r12

=

G(4m)

(r−r1)2

or r−r1=2r1
⇒r=3r1or r1=

r

3

∴ Gravitational potential at point C cause of mass M,
V=−

GM

r

∴ For M=m,V1=−

Gm

r1

or V1=

−Gm

r∕3

=

−3Gm

r

For M=4m,V2=

−G(4m)

(r−r1)

=

−G(4m)

r−r∕3

or V2=

−6Gm

r

Hence, net gravitational potential at point C,
Vnet =V1+V2 =

−3Gm

r

+(

−6Gm

r

)=−

9Gm

r