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A plank of mass M is placed over smooth ...

A plank of mass `M` is placed over smooth inclined plane and sphere is also placed over the plank. Friction is sufficient between sphere and plank. If plank and sphere are released from rest, the frictional force on sphere is -
.

A

up the plane

B

down the plane

C

horizontal

D

zero

Text Solution

Verified by Experts

The correct Answer is:
D
Case :
(1) we suppose friction is acting as shown in figure.

Point of contact must be at rest
`a_(p) = a_(p)'` …(1)
`a_(p) = g sin theta -(f)/(m)-R alpha rArr a_(p) = g sintheta -(f)/(m) -R (tau)/(I)`
`a_(p) = g sin theta - (f)/(m) -R (Rf)/(I) rArr a_(p) = g sin theta - (f)/(m) (1 +(mR^(2))/(I))`
`a_(p)' = g sin theta + (f)/(m) rArr for a_(p) = a_(p)' rArr f = 0`
Case- II

`a_(p) = (mg sin theta + f)/(m) + R (Rf)/(I)`
`a_(p) = g sin theta + (f)/(m) (1 + (mr^(2))/(I))`
`a_(p)' = g sin theta -(f)/(m) for a_(p) = a_(p) rArr f = 0`.
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