Home
Class 12
PHYSICS
A uniform rod of mass m and length L lie...

A uniform rod of mass m and length L lies radialy on a disc rotating with angular speed `omega` in a horizontal plane about vertical axis passing thorugh centre of disc. The rod does not slip on the disc and the centre of the rod is at a distance 2L from the centre of the disc. them the kinetic energy of the rod is

A

`1/2m omega^(2)(R^(2) + L^(2)/12)`

B

`1/2 M omega^(2)R^(2)`

C

`1/24 M omega^(2) L^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Moment of inertia of the rod w.r.t. the axis through the centre of the disc is (by parallel axis theorem),
`I =(mL^(2))/12 + mR^(2)` K.E. of the rod `=1/2 Iomega^(2) = 1/2 m omega^(2) [R^(2) + L^(2)/12]`
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise LEVEL - 2 (Angular Momentum, Collision)|20 Videos

  • ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|58 Videos

  • ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise LEVEL - 2 (Torque, Fixed and Rotation)|10 Videos

  • REVISION TEST-2 JEE

    VMC MODULES ENGLISH|Exercise PHYSICS|25 Videos

  • SIMPLE HARMONIC MOTION

    VMC MODULES ENGLISH|Exercise 7-previous year question|46 Videos

Similar Questions

Explore conceptually related problems

A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity omega about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is

A thin uniform copper rod of length l and mass m rotates uniformly with an angular velocity omega in a horizontal plane about a vertical axis passing through one of its ends. Determine the tension in the rod as a function of the distance r from the rotation axis. Find the elongation of the rod.

A uniform disc of radius a and mass m, is rotating freely with angular speed omega in a horizontal plane about a smooth fixed vertical axis through its centre. A particle, also of mass m, is suddenly attached to the rim of the disc of the disc and rotates with it. The new angular speed is

A uniform rod of mass m and length L is free to rotate in the vertical plane about a horizontal axis passing through its end. The rod initially in horizontal position is released. The initial angular acceleration of the rod is:

A horizontal disc is rotating about a vertical axis passing through its centre. If an insect moves from centre to rim then the angular momentum of the system

A uniform of mass m and length L is tied to a vertical shaft. It rotates in horizontal plane about the vertical axis at angular velocity omega . How much horizontal force does the shaft exert on the rod?

A uniform rod of mass m and length l_(0) is rotating with a constant angular speed omega about a vertical axis passing through its point of suspension. Find the moment of inertia of the rod about the axis of rotation if it make an angle theta to the vertical (axis of rotation).

A uniform disc is rotating at a constantt speed in a vertical plane about a fixed horizontal axis passing through the centre of the disc. A piece of the disc from its rim detaches itself from the disc at the instant when it is at horizontal level with the centre of the disc and moving upward. Then about the fixed axis, the angular speed of the

An uniform disc is rotating at a constant speed in a vertical plane about a fixed horizontal axis passing through the centre of the disc. A piece of the disc from its rim detaches itself from the disc at the instant when it is at horizontal level with the centre of the disc and moving upwards, then about the fixed axis. STATEMENT-1 : Angular speed of the disc about the aixs of rotation will increase. and STATEMENT-2 : Moment of inertia of the disc is decreased about the axis of rotation.

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.