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A rope remains wrapped over the circumfe...

A rope remains wrapped over the circumference of a wheel of radius r and of moment of inertia `I` about its axis. If a mass m is suspended from the lower end of the rope what will be the angular acceleration of the wheel ?

Text Solution

Verified by Experts

The correct Answer is:
`(mgr)/(1+mr^(2))`
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Knowledge Check

  • Moment of inertia of a circular wire of mass m and radius r about its diameter is

    A
    `(1)/(2)mr^(2)`
    B
    `(1)/(4) mr^(2)`
    C
    `mr^(2)`
    D
    `2 mr^(2)`

  • Moment of inertia of a circular ring of mass m and radius r about the normal axis passing through its centre is

    A
    `(mr^(2))/(4)`
    B
    `mr^(2)`
    C
    `(mr^(2))/(2)`
    D
    `(3)/(2) mr^(2)`

  • Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is

    A
    `(2)/(3) Mr^(2)`
    B
    `(2)/(5) Mr^(2)`
    C
    `Mr^(2)`
    D
    `(1)/(2)Mr^(2)`

    • Similar Questions

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    Find the moment of inertia of a ring of mass m and radius r about an axis passing through the tangent to the circle of the ring.

    Starting from rest, a wheel, with uniform acceleration, attains an angular velocity of 60 rad cdot s^(-1) at the end of 30 complete revolutions. What is the angular acceleration of the wheel?

    A round uniform body of radius R , mass M and moment of inertia I rolls down (without slipping ) an inclined plane making an angle theta with the horizontal. Then what will be its acceleration ?

    If the moment of inertia of a solid sphere of mass M and radius R is (2)/(5) MR^(2) , what will be the radius of gyration?.

    An automobile moves on a road with a speed of 54 km h.1. The radius of its wheels is 0.45m and the moment of inertia of the wheel about its axis of rotation is 3 kgm2. If the vehicle is brought to rest in 15s the magnitude of average torque transmitted by its brakes to the wheel is

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