Two friends `A` and `B` (each weighing `40 kg`) are sitting on a frictionless platform some distance d apart. A rolls a ball of mass `4 kg` on the platform towards `B` which `B` catches. Then `B` rolls the ball towards `A` and `A` catches it. The ball keeps on moving back and forth between `A` and `B`. The ball has a fixed speed of `5 m//s` on the platform.
a. Find the speed of `A` after he rolls the ball for the first time.
b. Find the speed of `A` after he catches the ball for the first time.
c. Find the speed of `A` and `B` after the ball has made five round trips and is held by `A`.
d. How many times can `A` roll the ball?
e. Where is the centre of mass of the system `A + B +` ball at. the end of the nth trip?

Options

A. `(10)/(11)d`
B. `(10)/(21)d`
C. `(50)/(11)d`
D. None of these

Answer

B

Explanation

from linear momentum conservation
`M_(A)V=m_(b)5rArr v=(4xx5)/(40)=0.5m//sAns.`
`F_(e x t)=0`, Centre of mass of system cannot move Initial position of centre of mass of `A`.

`X_(cm)=(40d)/(44+40)=(10)/(21)d`