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Tulsi Rout
Asked: 2022-11-07T11:47:49+05:30 In:

A disc of mass `m` and radius `R` is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass `m//2` each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity `omega_(0)` and released.
image
The angular speed of the disc when the balls reach the end of the disc is
A. `(omega_(0))/2`
B. `(omega_(0))/3`
C. `(2omega_(0))/3`
D. `(omega_(0))/4`

A disc of mass `m` and radius `R` is free to rotate in a horizontal plane about a vertical smooth fixed axis passing through its centre. There is a smooth groove along the diameter of the disc and two small balls of mass `m//2` each are placed in it on either side of the centre of the disc as shown in Fig. The disc is given an initial angular velocity `omega_(0)` and released.
image
The angular speed of the disc when the balls reach the end of the disc is
A. `(omega_(0))/2`
B. `(omega_(0))/3`
C. `(2omega_(0))/3`
D. `(omega_(0))/4`
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1 Answer

  1. Correct Answer – B
    Let the angular speed of the disc when the balls reach the end be `omega`. From conservation of angular momentum,
    `1/2mR^(2)omega_(0)=1/2mR^(2)omega+m/2R^(2)omega+m/2R^(2)omega`
    or `omega=(omega_(0))/3`

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