A circular hole of radius $(\frac{a}{2})$ is cut 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:

Option 1 -

$\frac{5}{6} a$

Option 2 -

$\frac{1}{6} a$

Option 3 -

$\frac{10}{11} a$

Option 4 -

$\frac{2}{3} a$

5 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

$= \frac{σ π a^{2} \times a - \frac{σ π a^{2}}{4} \times \frac{3 a}{2}}{σ π a^{2} - \frac{σ π a^{2}}{4}} = \frac{\frac{5}{8} σ π a^{3}}{\frac{3}{4} σ π a^{2}} = \frac{5}{8} σ π a^{2} \times \frac{4}{3} σ π a^{2} = \frac{5}{6} a$

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A circular hole of radius $(\frac{a}{2})$ is cut 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:

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A circular hole of radius ( a 2 ) is cut 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:

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A circular hole of radius $(\frac{a}{2})$ is cut 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: