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A particle of mass m is projected up fro...


A particle of mass `m` is projected up from the bottom of an inclined plane with initial velocity `v_(0)` at angle `45^(@)` with an inclined plane of inclination `30^(@)` as shown in figure. At the same time a small block of same mass `m` is released from rest at a height `h`, the particle hits the block at some point on the inclined plane. Neglect friction at inclined.
Q. The value of height h is

A

`(v_(0))/(sqrt(2))`

B

`(v_(0))/(2)`

C

`(v_(0))/(2sqrt(2))(1-(4)/(sqrt(3)))`

D

`(v_(0))/(2sqrt(2))(1+(4)/(sqrt(3)))`

Text Solution

Verified by Experts

The correct Answer is:
C
From conservation of momentum along the inclined plane
`mv_(x)+mv_(x)=2mv_(f)`
`v_(f)=(v_(x)-v_(x)^('))/(2)=(1)/(2)[(v_(0))/(sqrt(2))-(g)/(2)(2sqrt(2)v_(0))/(sqrt(3)g)-(g)/(2)(2sqrt(2)v_(0))/(sqrt(3)g)]=(v_(0))/(2sqrt(2))(1-(4)/(sqrt(3)))`
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