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A uniform disc of radius R is spinned to...

A uniform disc of radius `R` is spinned to the angular velocity `omega` and then carefully placed on a horizontal surface. How long will the disc be rotating on the surface if the friction coeffiecient is equal to `k`? The pressure exerted by the disc on the surface can be regarded as uniform.

A

`(4omega R)/(3 mu g)`

B

`(3omega R)/(4 mug)`

C

`(omega R)/(3 mu g)`

D

`(4 omega R)/(mu g)`

Text Solution

Verified by Experts

The correct Answer is:
B
df = friction force on elements ring area.
`df = mu(dN)`
`=mu (m/(piR^(2)) 2 piu xx dx)g = (2mu m gx dx)/(R^(2))`
Then, torque of this df, `d tau = x df =(2mu m gx^(2))/R^(2) dx`

`tau = int dt = int_(0)^(R) (2mu m g x^(2)dx)/R^(2) = 2/3 mu mg R , tau =Ialpha rArr 2/3 mu gR = (mR^(2))/2 alpha rArr alpha =4/3 (mug)/R`
We know, `omega = omega_(0) + alpha t, 0=alpha -4/3 (mu g)/R t rArr t-(3omega R)/(4 mug)`
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