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`.

After starting from end B of the rod the spider reaches the end A at a time

Options

A. (a) `40s`
B. (b) `30s`
C. (c) `80s`
D. (d) `10s`

Answer

C

Explanation

`t=t_1+t_2=((4L)/(v))+((12L-4L)/(v//2))=(20L)/(v)`
But `L/v=T=4s`
`:. t=80s`