A small block of mass M moves on a frictionless surface of an inclined plane as shown in the figure. The angle of the incline suddenly changes from `60^@` to `30^@` at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic. The speed of the block at point B immediately after it strikes the second incline is

Options

A. `sqrt(120) m//s`
B. `sqrt(105) m//s`
C. `sqrt(90)m//s`
D. `sqrt(75) m//s`

Answer

D

Explanation

Height fallen by the block from `B` to `C`
`h_(2)=3sqrt(3) tan30^(@)=3m`
Let `v_(3)` be the speed of the block, at point `C` just before it leaves the second incline, then
`v_(3)=sqrt(v_(2)^(2)+2gh_(2))=sqrt(45+2xx10xx3)=sqrt(105) m//s`