A uniform bar of length `12 L` and mass `48 m` is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass `8m` is sitting on end `A` of the rod and a spider (an insect) of mass `16 m` is sitting on the other end `B`. Both the insects start moving towards each other along the rod with moth moving at speed `2v` and the spider at half of this speed. 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 the insect. Also, let `v = L//T`, where `T` is a constant having value `4 sec`.

Displacement of the rod by the time when the insects meet is

Options

A. `L//2`
B. `L`
C. `3L//4`
D. zero

Answer

C

Explanation

`P_("moth") = 8m(2v) = 16mv` , `P_("spider") =16mv`
`P_("system") = 0` here rod does not move.