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A particle is placed at rest inside a ho...

A particle is placed at rest inside a hollow hemisphere of radius R. The coefficient of friction between the particle and the hemisphere is `mu=(1)/(sqrt(3))`. The maximum height up to which the particle can remain stationary is

A

`(R )/(2)`

B

`(1-(sqrt3)/(2))R`

C

`(sqrt3)/(2)R`

D

`(3R)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
B
`h=R- R cos theta,mu=Tan theta`
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Knowledge Check

  • A partical is placed at rest inside a hollow hemisphare of redius R . The coefficient of friction between the partical and the homisphere is mu = (1)/sqrt(3) . The maximum height up to which the partical can remain stationary is

    A
    `(R )/(2)`
    B
    `(1 - sqrt(3)/(2)) R`
    C
    `sqrt(3)/(2) R`
    D
    `(3 R)/(8)`

  • The coefficient of friction between an insect and a hemispherical bowl of radius r is mu . The maximum height to which the insect can crawl in the bowl is

    A
    `( r )/( sqrt( 1+ mu^(2)))`
    B
    `r[1-(1)/( sqrt( 1+ mu^(2)))]`
    C
    `r sqrt( 1+ mu^(2))`
    D
    `r[ sqrt( 1+ mu^(2))-1]`

  • A particle is released from the top of the smooth hemisphere R as shown. the normal contact between the particle and the hemisphere in position theta is

    A
    `mg(3-2costheta)`
    B
    `mg(3cos theta-2)`
    C
    `mg(4costheta-3)`
    D
    `mg(4-3costheta)`