Q.

A uniform cylinder of mass M and radius R is placed on a rough horizontal board, which in turn is placed on a smooth surface. The coefficient of friction between the board and the cylinder is μ. If the board starts accelerating with constant acceleration a, as shown in the figure, then

Moderate

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By Expert Faculty of Sri Chaitanya

for pure rolling motion of the cylinder, direction of frictional force is forward and its magnitude is Ma/3

the maximum value of a, so that the cylinder performs pure rolling is 3 μg

the acceleration of the centre of mass of the cylinder under pure rolling condition for the given a is a/3

the acceleration of the centre of mass of the cylinder under pure rolling condition for the given a is a/8.

answer is 1,2,3.

(Detailed Solution Below)

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Detailed Solution

Let the frictional force be in the forward direction, thenf=Ma0and fR=MR22α0a0=fM and α0=2fMRFor pure rolling, a0+Rα0=afM+2fM=a⇒f=Ma3For pure rolling, f

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