Two bodies of masses 4 ~m and 9 ~m are separated by a distance ' r '. The gravitational potential at a point on this line joining them where the gravitational field becomes zero is

Step-by-step solution

At the position when the gravitational field is zero. (Distance x is measured from 4 ~m mass) aligned & G(4 ~m ) x^2 = G(9 ~m ) (r-x)^2 & 4 9 = ( x r-x )^2 2 3 = x r-x & 2 r-2 x=3 x 2 r=5 x x= 2 r 5 aligned The point P is at a distance 2 r 5 from mass 4 ~m and (r- 2 5 r )= 3 r 5 from mass m . aligned & v=- G(4 ~m ) ( 2 5 r ) - G(9 ~m ) 3 r 5 = -5 G m r [ 4 2 + 9 3 ] & = -5 G m r [2+3] =-25 G m r aligned