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 `C` immediately before is leaves the second incline is

Options

A. `sqrt(120) m//s`
B. `sqrt(105) m//s`
C. `sqrt(90) m//s`
D. `sqrt(75) m//s`

Answer

B

Explanation

In `delta BCE, tan 30^(@) = (BE)/(CE) rArr (1)/(sqrt(3) = (BE)/(3sqrt(3) rArr BE = 3m `
Appling mechanical energy conservation Machanical energy at `B = ` Machinical energy is `C`
`(1)/(2) M(sqrt(45)^(2) + M xx 10 xx 3 = (1)/(2) Mv_(C)^(2)`
`45 + 60 = v_(C)^(2) :. v_(2) = sqrt(105)m//s `