First slide

Rolling motion

Question

A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are the same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by

Moderate

A

the solid sphere
B

the hollow sphere
C

the disc
D

all will take the same time

Solution

Since linear acceleration is the same for all $(a = M g \sin θ - μ M g \cos θ)$ as they have the same mass ‘M’ and the same ' $μ$ ' .
Hence, all will reach the bottom simultaneously. Hence (d).

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