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A uniform plate of mass M stays horizont...

A uniform plate of mass M stays horizontally symmetrically on two wheels rotating in opposite directions. The separation between the wheels is L. the friction coefficient between each and the plate is `mu`. Find the time period of oscillation of the plate if it is slightly displaced along its length and released.

Text Solution

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Let the plate be displaced towards right by x and released.

`N_1+N_2=mg`
Taking torque about A
`N_2L=mg(L/2+x)`, `N_2=mg(1/2+x/L)`
`N_1=mg(1/2-x/L)`
Restoring force
`F=-(f_2-f_1)=-mu(N_2-N_1)=-mu(2mgx)/(L)`
`a=F/m=-(2mug)/(L)x=-omega^2x`
`T=2pi((L)/(2mug))`
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Knowledge Check

  • The coin is notating with a plate without sliding If the coefficient of friction between the coin and plane is mu = 0.75 the friction between the coin and plate is If the plate is rotating along and the coin is gently placed on the rotating plate, the frictional force on the coin is

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