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 s of A and B after the ball has made 5 round trips and is held by A. d. How many times can A roll theball? e. where is the centre of mas the system A+B+ ball at the end of the nth trip?

Options

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

Answer

C

Explanation

from linear momentum conservation
`M_(A)V=m_(b)5rArr v=(4xx5)/(40)=0.5m//sAns.`
`m_(A)0.5+m_(b)5=(M_(A)+m_(b))=V_(1)`
`V=(40xx0.5+4xx5)/(44)=(40)/(44)=(10)/(11)m//s Ans. `