Home
Class 12
PHYSICS
A uniform cylinder of radius R is spinne...

A uniform cylinder of radius `R` is spinned about it axis to the angular velocity `omega_(0)` and then placed into a corner,. The coeficient of friction between the corner walls and the cylinder is `mu_(k)` How many turns will the cylinder accomplish before it stops?

A

`(1+mu_(k)^(2)omega_(0)^(2)R)/(pi mu_(k)(1+mu_(k))g)`

B

`((1+mu_(k)^(2))omega_(0)^(2)R)/(8pi mu_(k)(1+mu_(k))g)`

C

`(8(1+mu_(k)^(2))omega_(0)^(2)R)/(pi mu_(k)(1+mu_(k))g)`

D

`(3(1+mu_(k)^(2))omega_(0)^(2)R)/(pi mu_(k)(1+mu_(k))g)`

Text Solution

Verified by Experts

The correct Answer is:
B
`theta =(0-omega_(0)^(2))/(-2(2gmu(1-mu))/(R(1+mu^(2)))) =Romega_(0)^(2)(1+mu^(2))/(4gmu(1+mu))`, No. of tunrns `=theta/(2pi) = (R omega^(2)(1+mu^(2)))/(8gmu(1+mu)pi)`
Promotional Banner

Topper's Solved these Questions

  • ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise LEVEL - 2 (General rigid body motion, Rolling)|10 Videos

  • ROTATIONAL MOTION

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

  • ROTATIONAL MOTION

    VMC MODULES ENGLISH|Exercise LEVEL - 2 (Rotatinal Kinematics, Moment of Inertia)|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 ring of radius R is first rotated with an angular velocity omega and then carefully placed on a rough horizontal surface. The coefficient of friction between the surface and the ring is mu . Time after which its angular speed is reduced to half is

A thin but very large plank of mass 2 m is placed on a horziontal smooth surface. A solid cylinder of mass m and radius r is given only translational velocity v_(0) and gently placed on the plank as shown in the figure. The coefficient of kinetic friciton between the plank and the cylinder is mu . the cylinder given impluse t=0, than at what time pure rolling starts

A uniform cylinder of mass M and radius R is placed on a rough horizontal board, which in turn is placed on a smooth surface. The coefficient of friction between the board and the cylinder is mu . If the board starts accelerating with constant acceleration a, as shown in the figure, then Option1 for pure rolling motion of the cylinder, direction of frictional force is forward and its magnitude is M a / 3 Option2 the maximum value of a, so that cyliner performs pure rolling is 3 μ g Option3 The acceleration of the centre of mass of te cylinder under pure rolling condition for the given a is a / 3 Option4 none of these

A cylinder of mass m radius R is spined to a clockwise angular velocity omega_(o) and then gently placed on an inclined plane for which coefficient of friction mu = tan theta, theta is the angle of inclined plane with the horizontal. The centre of mass of cylinder will remain stationary for time

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 solid cylinder of mass M and radius R rotates about its axis with angular speed omega . Its rotational kinetic energy is

A disc of radius R is spun to an angular speed omega_(0) about its axis and then imparted a horizontal velocity of magnitude (omega_(0)R)/(4) (at t=0 ) with its plane remaining vertical. The coefficient of friction between the disc and the plane is mu . The sense of rotation and direction of its linear speed are shown in the figure. The disc returns to its initial point in time T=(25)/(6k mug)omega_(0)R . Find the value of k .

A disc of the radius R is spun to an angular speed omega_0 about its axis and then imparted a horizontal velocity of magnitude (at t = 0) with its plane remaining vertical. The coefficient of friction between the disc and the plane is mu . The sense of rotation and direction of its linear speed are shown in the figure . Choose the correct statement.

A hollow vertical cylinder of radius R is rotated with angular velocity omega about an axis through its centre. What is the minimum coefficient of static friction between block M and cylinder wall necessary to keep the block suspended on the inside of the cylinder ?

A cylinder of water, is rotating about its own axis with uniform angular velocity ω. The shape of free surface of water will be