First slide

Dynamics of rotational motion about fixed axis

Question

A solid cylinder S and a hollow cylinder T of same mass and same outer radius have a thin thread wound over them. One end of each thread is fixed to the same ceiling. They are initially held at rest with their axis horizontal and parallel to each other, at same height above ground. tf the cylinders are released simultaneously with strings taut then the correct statement is :

Moderate

A

S will reach ground earlier than f
B

T will reach ground earlier than S
C

Both will reach ground together
D

For small height S will reach earlier and for large height T will reach earlier

Solution

mg -T = ma
$TR = Iα and a = Rα$
Solving, we get
$a = \frac{mg}{(m + \frac{I}{R^{2}})}$
So, due to greater 1 of hollow cylinder, its acceleration (a) is lesser and hence, it will fall slowly than solid cylinder.

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