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A larger spherical mass M is fixed at on...

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

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The correct Answer is:
7
From FBD of middle mass: `(GMm)/(9l^2)-(Gm^2)/l^2-T=ma`
Since T=0, `(GMm)/(9l^2) -(Gm^2)/l^2 =ma` ….(i)
Also , for the right most mass :
`(GMm)/(16l^2) + (Gm^2)/l^2 = ma` …(ii)
Equating (i) and (ii) , `(GMm)/(9l^2)-(GMm)/(16l^2)=(2GM^2)/(l^2) rArr m=(7M)/288`
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