A uniform bar of length `12L` and mass `48m` is supported horizontally on two fixed smooth tables as shown in figure. A small moth (an insect) of mass `8m` is sitting on end A of the rod and a spider (an insect) of mass `16m` is sitting on the other end B. Both the insects moving towards each other along the rod with moth moving at speed `2v` and the spider at half this speed (absolute). They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity `v/2` relative to the rod towards the end A. The spider takes negligible time in eating on the other insect. Also, let `v=L/T` where T is a constant having value `4s`.

By what distance the centre of mass of the rod shifts during this time?

Options

A. (a) `(8L)/(3)`
B. (b) `(4L)/(3)`
C. (c) `L`
D. (d) `L/3`

Answer

A

Explanation

Till `t_1`, rod is stationary. For time `t_2` rod is moving with absolute speed `u(=v//6)`
`:.` Displacement of rod `=(v/6)t_2`
`=(v/6)((16L)/(v))=(8L)/(3)`