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A particle of mass m initially at rest s...

A particle of mass `m` initially at rest starts moving from point `A` on the surface of a fixed smooth hemisphere of radius `r` as shown. The particle looses its contact with hemisphere at point `B.C` is centre of the hemisphere. The equation relating `theta` and `theta'` is
.

A

`3sinalpha=2cosbeta`

B

`2sinalpha=3cosbbeta`

C

`3sinbeta=2cosalpha`

D

`2sinbeta=3cosalpha`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `v` be the speed of particle at `B`, just when it is about to loose contact.
From application of Newton's second law to the particle normal to the spherical surface.
`(mv^(2))/r=mgsinbeta`……….(1)
Applying conservation of energy as the block moves from `A` to `B`.
`1/2mv^(2)=mg(rcosalpha-rsinbeta)` .....(2)
Solving 1 and 2 we get
`3sinbeta=2cosalpha`
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