Home
Class 11
PHYSICS
A compound sphere is made by joining a h...

A compound sphere is made by joining a hemispherical shell and a solid hemisphere of same radius `R` and same mass as shown in figure. This system is kept between two smooth parallel walls and a smooth floor with the hollow hemisphere on the top as shown in figure. The maximum angular velocity of the compound shere when the system is slightly disturbed is `(` all surfaces are smooth `)`

A

`sqrt((15g)/(64R))`

B

`sqrt((15g)/(32R))`

C

`sqrt((15g)/(16R))`

D

`sqrt((15g)/(8R))`

Text Solution

Verified by Experts

The correct Answer is:
B
Change in `PE=` Increase in `K.E.`
`Mg[(R)/(2)2-(3R)/(8)2]=(1)/(2)[(2)/(5)MR^(2)+(2)/(3)MR^(2)]omega^(2)(g)/(4)`
`=(2)/(2)[(1)/(5)+(1)/(3)]Romega^(2) sqrt((15g)/(32R))=omega`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise DPP 65|5 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 66|4 Videos

  • DAILY PRACTICE PROBLEMS

    RESONANCE|Exercise dpp 63|5 Videos

  • CURRENT ELECTRICITY

    RESONANCE|Exercise Exercise|54 Videos

  • ELASTICITY AND VISCOCITY

    RESONANCE|Exercise Advanced Level Problems|9 Videos

Similar Questions

Explore conceptually related problems

Inside a smooth spherical shell of the radius R a ball of the same mass is released from the shown position (Fig.) Find the distance travelled by the shell on the horizontal floor when the ball comes to the lowest point of the shell.

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 .

Knowledge Check

  • A hemispherical cavity of radius R is created in a solid sphere of radius 2R as shown in the figure . Then y -coordinate of the centre of mass of the remaining sphere is

    A
    `Y_("CM")=-R/15`
    B
    `Y_("CM")=-R/40`
    C
    `Y_("CM")=-R/30`
    D
    `Y_("CM")=-R/20`

  • A unofrom rope of mass m is placeced on a smooth fixed sphere of radius R as shown in the figure .Find the tension T in the rope when it is in a horizontal plane at a vertical distance h=R/2 below the top of the sphere .

    A
    `(mg)/(2pi)`
    B
    `(mg)/(2)`
    C
    `(sqrt3mg)/(2)`
    D
    `(sqrt3mg)/(2pi)`

  • A small sphere S of radius ,r and mass m rolls without slipping, inside a large hemispherical bowl B of radius R as shown in figure. S starts from rest at the top point of the hemisphere

    A
    The fraction of translational kinetic energy at the sphere is 5/7.
    B
    The fraction of rotational kinetic energy of the sphere is 2/7.
    C
    The fraction of rotational kinetic energy of the sphere is `2/7mv^(2)`.
    D
    The total kinetic energy of the sphere at the bottom of the bowl is `2/7mv^(2)`

    • Similar Questions

    Explore conceptually related problems

    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

    Two particles each of mass M are connected by a massless rod. The rod is lying on the smooth horizontal surface. If one of the particle is given an impulse MV as shown in the figure then angular velocity of the system would be:

    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 ball of mass m and radius r rolls inside a fixed hemispherical shell of radius R . It is released from rest from point A as shown in figure. The angular velocity of centre of the ball in position B about the centre of the shell is. .

    A small block of mass m is released from rest from position A inside a smooth hemispherical bowl of radius R as shown in figure. Choose the wrong option (s)

    Home
    Profile