Home
Class 11
PHYSICS
A block of mass m slides 0n a frictionle...

A block of mass `m` slides 0n a frictionless table. It is constrained to move inside a ring of radius `R` . At time `t=0` , block is moving along the inside of the ring (i.e. in the tangential direction) with velocity `v_(0)` . The coefficient of friction between the block and the ring is `mu` . Find the speed of the block at time `t` .

Text Solution

Verified by Experts

The correct Answer is:
A
`N=(mv^(2))/(R)`
`f_(max)=muN=(mumv^(2))/(R)`
:. Retardation `a=(f_(max))/(m)`
`=(muv^(2))/(R)`
:. `(-(dv)/(dt))=(muv^(2))/(R)`
or `int_(v_(0))^(v)(dv)/(v^(2))=-(mu)/(R)int_(0)^(t)dt`
or `v=(v_(0))/(1+(muv_(0)t)/(R))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CIRCULAR MOTION

    DC PANDEY|Exercise Subjective Questions|2 Videos

  • CIRCULAR MOTION

    DC PANDEY|Exercise JEE Main|23 Videos

  • CIRCULAR MOTION

    DC PANDEY|Exercise Level 2 Comprehension Based|5 Videos

  • CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

    DC PANDEY|Exercise Level 2 Subjective|21 Videos

  • COMMUNICATION SYSTEM

    DC PANDEY|Exercise Only One Option is Correct|27 Videos

Similar Questions

Explore conceptually related problems

A semicircular ring of radius R is fixed on a smooth horizontal table. A small block is projected with speed u so as to enter the ring at end A. Initial velocity of the block is along tangent to the ring at A and it moves on the table remaining in contact with the inner wall of the ring. The coefficient of friction between the block and the ring is mu . (a) Find the time after which the block will exit the ring at B. (b) With what speed will the block leave the ring at B.

A block of mass m is kept on horizontal turn table at x distance from the centre. If coefficient of friction between block and surface of turn table is mu , then maximum angular speed of the table so that block does not slip

Knowledge Check

  • A block of the mass of 1 kg is moving on the x -axis. A force F acting on the block is shown. The veloity of the block at time t = 2 s is -3ms^(-1) . What is the speed of the block at time t = 4 s?

    A
    `8ms^(-1)`
    B
    `2ms^(-1)`
    C
    `3ms^(-1)`
    D
    `5ms^(-1)`

  • A block of mass m is given an initial downward velocity v_(0) and left on inclined place ( coefficient of friction =0.6). The block will

    A
    continue of move down the plane with constant velocity `v_(0)`
    B
    accelerate downward
    C
    decelerate and come to rest
    D
    first accelerate downward then decelerate

  • A block is gently placed on a conveyor belt moving horizontal with constant speed After t = 4s the velocity of the block becomes equal to velocity of the belt If the coefficient of friction between the block and the belt is mu = 0.2 , then the velocity of the conveyor belt is .

    A
    `8//s`
    B
    `6m//s`
    C
    `4m//s`
    D
    `2m//s`

    • Similar Questions

    Explore conceptually related problems

    A block of mass m is pushed with a velocity v_(0) along the surface of a trolley car of mass M . If the horizontal ground is smooth and the coefficient of kinetic friction between the block of plank is mu . Find the minimum distance of relative sliding between the block and plank.

    A block of mass m is at rest on a rough inclined plane of angle of inclination theta . If coefficient of friction between the block and the inclined plane is mu , then the minimum value of force along the plane required to move the block on the plane is

    A block B is pushed momentarily along a horizontal surface with an initial velocity v . If mu is the coefficient of sliding friction between B and the surface, block B will come to rest after a time:

    A block A of mass m_1 rests on a horizontal table. A light string connected to it passes over a frictionless pully at the edge of the table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is H. When the block A is sliding on the table, the tension in the string is

    A block of mass M slides on a frictionless surface with an initial speed of v_(0) . On top of block is a small box of mass m (moving together with M with same speed v_(0) ). The coefficients of friction between box and block are mu_(s) and mu_(k) . The sliding block encounters an ideal spring with force constant k. Answer following question. What is maximum value of k for which it remains true that box does not slide ?

    Home
    Profile