A ball of mass m is attached to the lower end of a vertical string whose upper end is fixed. An identcial ball 'B' moving with a velocity `v_(0) = 6 m//s` at an angle `theta = 45^(@)` from vertical collides elastically with the ball 'A' as shown.
The verocity of the ball 'B' just after collision is

Options

A. `5 m//s`
B. `4 m//s`
C. `3 m//s`
D. `2 m//s`

Answer

D

Explanation

Using conservation of momentum of the system along horizontal direction
`(mv_(0))/(sqrt2) = mv^(2) - (mv_(1))/(sqrt2)`
`sqrt2v_(2) - v_(1) = v_(0)` ……(i)
`v_(2) cos 45^(@) + v_(1) = v_(0)`
`(v_(2))/(sqrt2) + v_(1) = v_(0)`
`sqrt2v_(2) + 2v_(1) = 2v_(0)` ......(ii)
Solving (i) and (ii) , we get
`3v_(1) = v_(0)`
`v_(1) = (v_(0))/(3) = (6)/(3) = 2 m//s`