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)`)

The speed of the block at point `B` immedutaly after it strikes the second inclime is -

Options

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

Answer

B

Explanation

`(h)/(sqrt3) = tan 60^(@) rArr h_(1) = 3m`
`(h_(2) - h_(1))/(3sqrt3) = tan30^(@) rArr h_(2) - h_(1) = 3 rArr h_(2) = 6m`
Velocity of block just before collision at B `= sqrt(2gh) = sqrt(2 xx 10 xx 3) = sqrt(60) ms^(-1)`

For totally inelastic collision velocity of block along normal to BC becomes zero adn since there is no impulse along BC becomes zero adn since there is no impulse along BC so momentum (velocity) along BC remains unchanged
Speed of block just after collision
`v_(B) = sqrt(60) cos 30^(@) = sqrt(60) xx (sqrt3)/(2) = sqrt(45) ms^(-1)`