First slide

Dynamics of rotational motion about fixed axis

Question

A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord. If we hang a body of mass m from the cord, the tangential acceleration of a point on rim of the disc is

Difficult

A

$\frac{mg}{M + m}$
B

$\frac{mg}{M + 2 m}$
C

$\frac{2 mg}{M + 2 m}$
D

$\frac{M + 2 m}{2 mg}$

Solution

Tangential aceleration
a = r $α = R (\frac{2 T}{MR}) = \frac{2 T}{M}$
T = $\frac{Ma}{2}$
Now mg-T = ma or mg-M $\frac{a}{2} = ma$
or mg = $(m + \frac{M}{2}) a or a = \frac{2 mg}{M + 2 m}$

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