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. `sqrt(60) m//s`
B. `sqrt(45) m//s`
C. `sqrt(30) m//s`
D. `sqrt(15) m//s`

Answer

B

Explanation

As the inclined plane is frictionless .
The K.E. at `B` = P.E. `at`A`
`(1)/(2) mv^(2) = mgh rArr v= sqrt(2gh)`

in `delta ADB , tan theta 60^(@) = (h)/(sqrt(3)`
`:. H = 3 m`
`:. V = sqrt(6g) = sqrt(60) m//s`
This is the velocity makes of the block just before collision . This velocity makes as angle of `30^(@)` with the vertical . Also is right angled triangle `BEC, /_ EBD = 60^(@)` Therefore `v` make an angle of `30^(@)` with the second inclined plase `BC` . THe componment of `v` along `BC` is a `cos 30^(@)`
It is given that the collision at `B` is parfectly indeatic therefore in impact force act normal to the plane such that the vertical along the incline `BC` remaine unchange and is equal to `v cos 30^(@)`
`= sqrt(60) xx (sqrt(180)/(4)) = sqrt(45) m//s`