Two massless string of length 5 m hang from the ceiling very near to each other as shown in the figure. Two balls `A` and `B` of masses `0.25kg` and `0.5kg` are attached to the string. The ball `A` is released from rest at a height `0.45m` as shown in the figure. The collision between two balls is completely elastic. Immediately after the collision, the kinetic energy of ball `B` is `1 J` The velocity of ball `A` just after the collision is

Options

A. `5ms^(-1)` to the right
B. `5ms^(-1)` to the left
C. `1ms^(-1)` to the right
D. `1ms^(-1)` to the left

Answer

D

Explanation

`(1)/(2)m_(B)v_(B)^(2)=K_(B)" "rArr" " (1)/(2)(0.5)v_(B)^(2)rArrv_(B)=2`
`v_(B)=(2m_(A))/(m_(A)+m_(B))u_(A)` and `v_(A)=(m_(A)-m_(B))/(m_(A)+m_(B))u_(A)`
`v_(A)=(m_(A)-m_(B))/(2m_(A))v_(B)=(0.25-0.5)/(0.5)xx2=-1m//s`