A small block of mass `M` move on a frictionless surface of an inclimed from as down is figure . The engle of the inclime suddenly change from `60^(@)` to `30^(@)` at point `B` . The block is initally at rest at `A` Assume the collsion between the block and the incline are totally inclassic `(g = 10m//s^(2)`)

If collision between the block and the incline is completely elestic , then the vartical (apward) component of the of the block at point `B` immediatly after it stricess the scond indine is -

Options

A. `sqrt(30) m//s`
B. `sqrt(15) m//s`
C. `0`
D. `-sqrt(15) m//s`

Answer

C

Explanation

In elastic collision, component of v1 parallel to BC will remain unchanged, while component perpendicular to BC will remain unchanged in magnitude but its direction will be reversed.
`v_(_|_) = v_1 cos 30^@ = (sqrt(60))((sqrt3)/2) = sqrt(45) m//s`
`v_(_|_) = v_1 sin 30^@ = (sqrt(60))(1/2) = sqrt(15) m//s`
Now the vertical component of velocity of the block,
`v' = v_(_|_) cos 30^@ = v_(||) cos 60^@" " = (sqrt15) ((sqrt3)/(2)) - (sqrt(45))(1/2) = 0`