Home
Class 11
PHYSICS
A uniform horizontal plank is resting sy...

A uniform horizontal plank is resting symmetrically in a horizontal position on two cylindrical droms , which are apinning in in opposite direction about their horizontal axes with equal angular velocity . The distance between the axes with equal angular velocity. The distance between the axes is `2 L` and the coefficient of friction between the plank and cylender is `mu` . If the plank is displaced slightly from the equilibrium position along its length and released, show that it performs simple horizontal motion. Caculate also the time period of motion.

Text Solution

AI Generated Solution

To solve the problem step by step, we will analyze the situation of the plank resting on two cylindrical drums and derive the equations governing its motion. ### Step 1: Understand the Setup - We have a uniform horizontal plank resting symmetrically on two cylindrical drums. - The distance between the axes of the drums is \(2L\). - The drums are rotating in opposite directions with equal angular velocity. - The coefficient of friction between the plank and the cylinders is \(\mu\). ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 4.1|23 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 4.2|23 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Single correct anwer type|14 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger|11 Videos

  • MISCELLANEOUS KINEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger type|3 Videos

Similar Questions

Explore conceptually related problems

A skater of mass m standing on ice throws a stone of mass M with a velocity of v in a horizontal direction. The distance over which the skater will move back (the coefficient of friction between the skater and the ice is mu )

The friction coefficient between plank and floor is mu . The man applies, the maximum possible force on the string and the system remains at rest. Then

A cylinder rests on a horizontal rotating disc, as shown in the figure. Find at what angular velocity, omega , the cylinder falls off the disc, if the distance between the axes of the disc and cylinder is R , and the coefficient of friction mugtD//h where D is the diameter of the cylinder and It is its height.

A uniform table of mas M stays horizontally and symmetrically on two wheels rotatig in opposite directions figure. The separsation between the wheels is L. The friction coefficeint between each whee, and the plate is mu . Find the time period of oscilationof the pate if it is slightly displaced along its length and released.

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 long horizontal plank of mass m is lying on a smooth horizontal surface. A sphere of same mass m and radius r is spinned about its own axis with angular velocity we and gently placed on the plank. The coefficient of friction between the plank and the sphere is mu . After some time the pure rolling of the sphere on the plank will start. Answer the following questions. Find the displacement of the plank till the sphere starts pure rolling.

A long horizontal plank of mass m is lying on a smooth horizontal surface. A sphere of same mass m and radius r is spinned about its own axis with angular velocity we and gently placed on the plank. The coefficient of friction between the plank and the sphere is mu . After some time the pure rolling of the sphere on the plank will start. Answer the following questions. Find the time t at which the pure roiling starts

A block of mass m is kept on a plank . The coefficient of friction between the plank and block is 1. The plank is slowly raised from one end so that it makes angle theta with horizontal . The forces of friction acting on the plank , when theta = 30 ^(@) and theta 60^(@) are respectively,

A rough horizontal plate rotates with angular velocity omega about a fixed vertical axis. A particle or mass m lies on the plate at a distance (5a)/(4) from this axis. The coefficient of friction between the plate and the particle is (1)/(3) . The largest value of omega^(2) for which the particle will continue to be at rest on the revolving plate is

A horizontal plank having mass m lies on a smooth horizontal surface. A sphere of same mass and radius r is spined to angular frequency omega_(0) and gently placed on the plank as shown in the figure. If coefficient of friction between the plank and the sphere is mu . Find the distance moved by the plank till sphere starts pure rolling on the plank. the plank is long enough.

Home
Profile