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A hemisphere of radius R and mass 4 m is...

A hemisphere of radius R and mass 4 m is free to slide with its base on a smooth horizontal table . A particle of mass m is placed on the top of the hemisphere . The angular velocity of the particle relative to centre of hemisphere at an angular displacement `theta` when velocity of hemisphere has become v is

A

`(5v)/(R "cos" theta)`

B

`(2v)/(R "cos" theta)`

C

`(3v)/(R "sin" theta)`

D

`(5v)/(R "sin" theta)`

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A hemisphere of radius R and of mass 4m is free to Slide with its base on a smooth horizontal table. A particle mass m is placed on the top of the hemisphere. Find the angular velocity of the particle relative to hemisphere at an angular displacement theta when velocity of hemisphere has become v .

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Knowledge Check

  • A particle of mass m is kept at the top of a smooth fixed sphere. It is given a horizontal velocity v then:

    A
    it will start moving along a circular path if `v lt sqrt(gR)`
    B
    it will start moving along a circular path if `v gt sqrt(gR)`
    C
    it will start moving along a parabolic path if `v lt sqrt(gR)`
    D
    it will start moving along a parabolic path if `v gt sqrt(gR)`

  • 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)`

  • A uniform solid hemisphere of radius 10 m and mass 64 kg is placed with its curved surface on the smooth horizontal surface and a string AB of length 4 m is attached to point A on its rim as shown in the figure Find the tension in the string if hemisphere is in equilibrium.

    A
    320 N
    B
    640 N
    C
    180 N
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