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

Between `A` and `B` height fallen by the block is
`h_(1)=sqrt(3)tan60^(@)=3m`
Hence speed of the block just before striking the second incline is
`v_(2)=sqrt(2gh_(1))=sqrt(2xx10xx3)=sqrt(60)m//s`

In perfectly inelastilc collision component of `v_(1)` perpendicular to `BC` will become zero, while component of `v_(1)` parallel of `BC` will remain unchanged.
`v_(2)="component of " v_(1)` along `BC`
`=v_(1)=cos30^(@)=(sqrt(60))((sqrt(3))/2)=(sqrt(45))=m//s`