Ball A of mass 50 gm and speed 10 m/s collides with other ball B of mass 10 gm and speed 15 m/s travelling in opposite direction with each other. Determine the final speed of ball B, if the coefficient of restitution is `2/5`.

Options

A. `(40)/(3)` m/s
B. `(75)/(3) m//s`
C. `(91)/(8)` m/s
D. `(85)/(6) m//s`

Answer

D

Explanation

Given, `m_(A)=50 gm, u_(A)=10m//s, m_(B)=10gm`
`u_(B)=-15m//s` and coefficient of restitution, `e=2/5`
The collision of ball A and B is shown as below,
`u_(A)=10 m//s " " u_(B)=15m//s`

Velocity of second ball B is given by the relation,
`v_(B)=(m_(A)(1+e))/(m_(A)+m_(B))u_(A)+(m_(B)-em_(A))/(m_(A)+m_(B))u_(B)`
Putting the given values in above relation, we get
`rArr v_(B)=(50(1+2/5))/(50+10)xx10+(10-50xx2/5)/(50+10)(-15)`
`rArr v_(B)=(50xx7xx10)/(60xx5)+(10xx15)/(60)`
`rArr v_(B)=(70)/(6)+(15)/(6)=(85)/(6) m//s`
Hence, the correct option is (d).