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)/(21)m//s,(50)/(11)m//s`
B. `(50)/(11)m//s,(10)/(11)m//s`
C. `(50)/(11)m//s,5m//s`
D. None of these

Answer

C

Explanation

from linear momentum conservation
`M_(A)V=m_(b)5rArr v=(4xx5)/(40)=0.5m//sAns.`
after through the ball velocity of man `A` is `0.5 m//s `
For man `B= 4xx5=40v_(2)-4xx5`
`rArr v_(2)=1m//s`
velocity `B` is `1m//s` after through the ball after through the ball second time, velocity of man `A` is
`4xx5+40xx0.5=40xxv_(3)-4xx5`
`v_(3)=1.5m//s`
similarlyy for man `B v_(4)=2m//s`
after 5 round trip and man `A` hold the ball velocity of man `B` is `5m//s`
velocity of man `A` ltbr. `4.5 xx 40+4xx5=(40+4)v_(5)`
`v_(5)=(50)/(11)m//s Ans. `