Home
Class 11
PHYSICS
The figure shows a system consisting of ...

The figure shows a system consisting of (i) a ring the outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed `omega` and (ii) an inner disc of radius 2R rotating anti clockwise with angular speed `omega//2.` The ring and disc are separated. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of `30^@` with the horizontal. Then with respect to the horizontal surface,

A

the point O has linear velocity `3 R omega hati`

B

the point P has linear velocity `(11)/(4)R omegahati+(sqrt3)/(4) R omega hatk.`

C

the point P has linear velocity `(13)/(4)R omega hati - (sqrt3)/(4)R omega hatk`

D

the point P has linear velocity `((3 - (sqrt3)/(4)) R omega hati + (1)/(4)R omega hatk.`

Text Solution

Verified by Experts

The correct Answer is:
A, B
(a,b) For rolling motion, the velocity of the point of contact
with respect to the surface should be zero. For this
`3Romega(-hati)|vecv_0 = 0 :. vecv_0 = 3Romegahati`

A shown in the figure, the point P will have two
velocities
(i) `3Romegahati` (due to translational motion)
(ii) `(R )/(2) omega` making an angle fo `30^@` with the vertical due
to rotation
`:. rarrup = [3R_omega hati - (R_oemga)/(4) hati]+(sqrt3R_omega)/(4) hatk`
`= (11)/(4) R_omega hati+ (sqrt3)/(4) R_omega hatk.`
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise MCQs with one correct answer|1 Videos

  • MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|63 Videos

  • SIMPLE HARMONIC MOTION

    SUNIL BATRA (41 YEARS IITJEE PHYSICS)|Exercise JEE Main And Advanced|69 Videos

Similar Questions

Explore conceptually related problems

A circular disc of radius r is rolling without slipping on a horizontal surface. What is the ratio of the translational KE and rotational KE of disc ?

A disc of radius R is moving on a rough horizontal surface with velocity v and angular speed omega at an instant as shown in figure. Choose the correct statement.

A ring and a disc of same mass roll without slipping along a horizontal surface with same velocity. If the K.E. of ring is 8J , then that of disc is

A disc of mass M and Radius R is rolling with an angular speed omega on the horizontal plane. The magnitude of angular momentum of the disc about origin is:

A disc of mass m and radius R rotating with angular speed omega_(0) is placed on a rough surface (co-officient of friction =mu ). Then

A thin circular ring of mass per unit length p and radius r is rotating at an angular speed omega as shown in figure. The tension in the ring is

A rough disc of mass m rotates freely with an angular velocity omega . If another rough disc of mass m/2 and same radius but spinning in opposite sense with angular speed omega is kept on the first disc. Then:

Assertion: A disc rolls without slipping on a horizontal surface and the linear speed of its centre of mass is v. The rotational speed of the particles on its rim at the top of the disc will be 2v. Reason: The disc rolls as if it is rotating about the point of contact with the horizontal surface.