A larger spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M. The point masses are connected by rigid massless rod of length l and this assembly is free to move along the line connecting them. All three masses interact only throght their mutual gravitational interaction. When the point mass nearer to M is at a distance r =3l form M, the tensin in the rod is zero for `m =k((M)/(288)).` The value of k is

Explanation

For the tension in the rod to be zero, the force on both
the masses m and m should be equal in magitude and
direction. Therefore

(GMm)/((4l))^2 + (Gmm)/(l^2) = (GMm)/((3l)^2 - (Gmm)/(l^2)`
`:. 2m =M[(1)/(9) - (1)/(16)]`
`:. m = (7M)/(288)`
K =7