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 many at rest at `A`. Assume that collisions between the block id the incline are totally inelastic.
The speed of the block at point `B` immediately after it strikes the second incline is

Options

A. `sqrt60` m/s
B. `sqrt45` m/s
C. `sqrt30` m/s
D. `sqrt15` m/s

Answer

B

Explanation

At point B the block has an inelastic collision with the incline, so component of velocity perpendicular to incline plane becomes zero and component parallel to second surface is retained. `h=sqrt3tan60^@ =3 m`
Velocity immediately after it strikes the second line
`v=sqrt(2gh) cos 30^@ =sqrt(2xx10xx3)xxsqrt3/2=sqrt45` m/s.