Question

Two bodies of masses m and 4m are placed at a distance r apart. The gravitational potential at the point where the gravitational field is zero is

Answer 1

Let the point be the position when the gravitational field is zero

Gmx2=G(4m)(r−x)2Gmx2=G(4m)(r−x)2

1x=2(r−x)1x=2(r−x)

r−x=2xr−x=2x

x=r3x=r3

the point P is at a distance r3r3 from mass m and 2r32r3 from mass 4m

V=−GMr3−G(4m)2r3V=−GMr3−G(4m)2r3

=−9GMr=−9GMr

Hence d is the correct answer