Discussion Forum

1)

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them.

 All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r=3l from M the tension in rod is zero for   $m=k\left(\frac{M}{288}\right)$  .The  value of k is

Answer:

Option D

Explanation:

For point mass at distance r=3l

$\frac{GMm}{(3l)^{2}}-\frac{Gm^{2}}{l^{2}}=ma$  ......(i)

 For point mass at distance r=4l

   $\frac{GMm}{(4l)^{2}}+\frac{Gm^{2}}{l^{2}}=ma$                ...........(ii)

 Equating  the two equations we have,

$\frac{GMm}{9l^{2}}-\frac{Gm^{2}}{l^{2}}=\frac{GMm}{16l^{2}}+\frac{Gm^{2}}{l^{2}}$

$\frac{7GMm}{144}=\frac{2Gm^{2}}{l^{2}}$

$m=\frac{7M}{288}$