Home
Class 11
PHYSICS
A hemispherical bowl of radius R is set ...

A hemispherical bowl of radius R is set rotating about its axis of symmetry which is kept vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surfaces of the bowl is smooth, and the angel made by the radius through the block with the vertical is `theta`, find the angular speed at which the bowl is rotating.

Text Solution

Verified by Experts

Suppose the angular speed of rotatioin of the bowl is `omega`. The block also moves with this angular speed. The forces on the block are ure.
a. the normal force N and
b. the weight mg

The block moves in a horizontal circle with the centre at C, so that teh radius is PC=OP `sintheta=Rsintheta.` Its acceleration is therefore `omega^2Rsintheta.` Resolving the forces along PC and applying Newton's second law,
`Nsintheta=momega^2Rsintheta`
`or, N=m omega^2R` ........i
As there is vertical acceleration,
`Ncostheta=mg`..........ii
Dividing i by ii
`1/(costheta)=(omega^2R)/g`
or, `omega=sqrt(g/(Rcostheta))`
Promotional Banner

Topper's Solved these Questions

  • CIRCULAR MOTION

    HC VERMA|Exercise Question for short Answer|10 Videos

  • CIRCULAR MOTION

    HC VERMA|Exercise Objective -1|16 Videos

  • CIRCULAR MOTION

    HC VERMA|Exercise Exercises|30 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM, COLLISION

    HC VERMA|Exercise Exercises|64 Videos

  • FLUID MECHANICS

    HC VERMA|Exercise All Questions|96 Videos

Similar Questions

Explore conceptually related problems

A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical.A small block is kept in the bowl at a position where the radius makes an angle theta with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is mu . Find the range of the angular speed for which the block will not slip.

A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I . The system is at rest when a friend throws as ball of mass m and the kid catches it. If the velocity of the ball is v horizontally along the tangent to the edge of the platform when it was caught by the kid find the angular speed of the platform after the event.

A particle of mass m is kept on the top of a smooth sphere of radius R. It is given a sharp impulse which imparts it a horizontal speed v. a. find the normal force between the sphere and the particle just after the impulse. B. What should be the minimum value of v for which the particle does not slip on the sphere? c. Assuming the velocity v to be half the minimum calculated in part, d. find the angle made by the radius through the particle with the vertical when it leaves the sphere.

A hemispherical bowl is made up of stone whose thickness is 5 cm. If the inner radius is 35 cm, find the total surface area of the bowl.

A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find ratio of its rotational energy to its total energy.

A disc of radius 10 cm is rotating about its axis at an angular speed of 20 rad/s. Find the linear speed of a. a point on the rim, b. the middle point of the radius.

A wheel of moment of inertia I and radius r is free to rotate about its centre as shown in figure. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The system is released from rest. Find the speed of the block as it descends through a height h.

A spherical solid ball of 1 kg mass and radius 3 cm is rotating about an axis passing through its centre with an angular velocity of 50 rad/s. Calculate the kinetic energy of rotation.

Figure shows as rod of length 20 cm pivoted near an end and which is made to rotate in a horizontal plane with a constant angular speed. A ball ofmass m is spuspended by a string angular also of length 20 cm from the other end of the rod. If the angle theta made by the stirng with the vertical is 30^0 . find the anglular speed of the rotation. Take g=10 m/s^2

In a rotor, a hollow vertical cylindrical structure rotates about its axis and a person rests against the inner wall. At a particular speed of the rotor, the floor below the person is removed and the person hangs resting against the wall without any floor. If the radius of the rotor is 2m and the coefficient of static friction between the wall and the person is 0.2, find the minimum speed at which the floor may be removed Take g=10 m/s^2 .