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Question

A uniform disc of mass M and radius R rolls down an inclined (angle of inclination=θ) plane without slipping then frictional force is given by kMgsinθ3,then the value of k,is

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Solution

f is the frictional force along the incline plane in upward direction
gsinθ is the acceleration in the downward direction
α is the angular acceleration for pure rotation
I=MR22 is the moment of inertia about center of mass.
For pure rolling motion,we have equation as
Mgsinθf=Ma (1)
Torque about center of mass
f.R=Iα
f.R=IaR as α=aR
f=MR2a2R2
f=Ma2 (2)
Multiplying equation (2) by 2 and subtracting from (1) we get,
2f+fMgsinθ=0
f=Mgsinθ3




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