First slide

Rolling motion

Question

A solid cylinder is rolling down a rough inclined surface with out slipping and it takes 3 sec to reach the bottom. Now mass of the cylinder is quadrupled and radius is doubled. If this cylinder is allowed to roll down the same inclined plane without slipping, then it will reach the bottom in time

Moderate

A

3 sec
B

6 sec
C

0.75 sec
D

1.5 sec

Solution

a = Acceleration of the axis of cylinder
$= \frac{gsinθ}{1 + \frac{{mR}^{2}}{\frac{1}{2} {mR}^{2}}} = \frac{1}{3} gsinθ$
So acceleration is independent of mass and radius of cylinder.

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