Home
Class 11
PHYSICS
A cord is wound around the circumference...

A cord is wound around the circumference of wheel of radius r. The axis of the wheel is horizontal and `MI` is `I`. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

A

`sqrt((2gh)/(I+mr^(2)))`

B

`((2mgh)/(I+mr^(2)))^(1//2)`

C

`((2mgh)/(I+2mr^(2)))^(1//2)`

D

`sqrt(2gh)`

Text Solution

Verified by Experts

The correct Answer is:
B
Velocity, `v = r omega`
Decrease in gravitational potential energy = Increase in kinetic energy

`:. mgh=(1)/(2)Iomega^(2)+(1)/(2)mv^(2)=(1)/(2)Iomega^(2)+(1)/(2)m(r omega)^(2)`
`:.` Angular velocity, `omega=sqrt((2mgh)/(I+mr^(2)))`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ROTATION

    DC PANDEY|Exercise (B) Chapter Exercises|25 Videos

  • ROTATION

    DC PANDEY|Exercise (C) Chapter Exercises|39 Videos

  • ROTATION

    DC PANDEY|Exercise Check point 9.3|15 Videos

  • RAY OPTICS

    DC PANDEY|Exercise Integer type q.|15 Videos

  • ROTATIONAL MECHANICS

    DC PANDEY|Exercise Subjective Questions|2 Videos

Similar Questions

Explore conceptually related problems

A cord is wound around the circumference of a wheel of diameter 0.3 m. The axis of the wheel is horizontal. A mass of 0.5 kg is attached at the end of the cord and it is allowed to fall from rest. If the weight falls 1.5 m in 4s, what is the angular acceleration of the wheel ? Also find out the moment of inertia of the wheel.

A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter 1 m . A mass of 2 kg is tied at the end of the cord and it is allowed to fall from rest. The weight falls 2 m in 4 s . The axle of the wheel is horizontal and the wheel rotates which its plane vertical. if g = 10 ms^(-2) , what is the angular acceleration of the wheel ?

Knowledge Check

  • A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and moment of inertia about it is l. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h, the angular velocity of the wheel will be

    A
    `sqrt((2gh)/(I + mr))`
    B
    `sqrt((2mgh)/(I + mr^(2)))`
    C
    `sqrt((2mgh)/(I+ 2mr^(2)))`
    D
    `sqrt(2gh)`

  • A cord is wound around the circumference of wheel of radius r the axis of the wheel is horizontal and moment of inerita about it is / The weight mg is attached to the end of the cord and falls from rest after falling throgh a distance h the angular velocity of the wheel will be

    A
    `[mgh]^(1//2)`
    B
    `[(2mgh)/(I+2mr^(2))]^(1//2)`
    C
    `[(2mgh)/(I+mr^(2))]^(1//2)`
    D
    `[(mgh)/(I+2mr^(2))]^(1//2)`

  • A cord is wound round the circumference of wheel of radius r . The axis of the wheel is horizontal and fixed and moment of inertia about it is I . A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h , the angular velocity of the wheel will be.

    A
    `sqrt((2 gh)/(I + mr))`
    B
    `[(2 mgh)/(I + mr^2)]^(1/(2))`
    C
    `[(2 mgh)/(I +2 m)]^(1/(2))`
    D
    `sqrt(2 gh)`

    • Similar Questions

    Explore conceptually related problems

    A cord of negligible mass is wound around the rim of a wheel of radius 20 cm. An object of mass 600 g is attached to the end of the cord and is allowed to fall from rest. It took 5 s for the object to fall by 2 m. Calculate the angular acceleration and moment of inertia of the wheel. Assume that the axis of wheel is horizontal.

    A cord is wound round the circumference of a solid cylinder radius R and mass M . The axis of the cylinder is horizontal. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h .

    A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be :-

    A cord is wound round the circumference of a wheel of radius r. The axis of the wheel is horizontal and its moment of inertia about this axis is I. A weight mg is attached to the end of the cord and is allowed to fall from rest. The angular velocity of the wheel, when the weight has fallen through a distance h, is

    A cord is wound round the circumference of a solid cylinder radius R and mass M . The axis of the cylinder is horizontal. A weight mg is attached to the end of the cord and falls from rest. After falling through a distance h . If the mass starts from rest and falls a distance h , then its speed at that instant is:

    Home
    Profile