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PhysicsCenter of MassCalculate of COMMedium2 minPYQ_2021

PhysicsMediumsingle choice

A circular hole of radius $(\frac{a}{2})$ is cut out of a circular disc of radius $a$ as shown in figure. The centroid of the remaining circular portion with respect to point $O$ will be:

Question diagram: A circular hole of radius a 2 is cut out of a circular disc

Options:

Answer:

B

Solution:

Let $σ$ be the uniform mass density of disc then

$x_{COM} = \frac{(σ π a^{2}) a - σ π (\frac{a^{2}}{4}) \times \frac{3 a}{2}}{σ π a^{2} - \frac{σ π a^{2}}{4}}$

$= \frac{a - \frac{3 a}{8}}{1 - \frac{1}{4}} = \frac{5 a}{6}$

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Calculate of COM

⏱ 2mℹ️ Source: PYQ_2021

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