First slide

Methods to locate centre of mass

Question

A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The centre of mass of the new disc is aR from the centre of the bigger disc. The value of a is

Moderate

A

$\frac{1}{2}$
B

$\frac{1}{3}$
C

$\frac{1}{4}$
D

$\frac{1}{6}$

Solution

shift in the center of mass = $\frac{m a s s r e m o v e d x i t s c o m}{m a s s r e m a i n} = \frac{\frac{m}{4} x R}{\frac{3 m}{4}} = R / 3 a = 1 / 3$ (mass of a disc is proportional to $R^{2}$

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