Question 133: Centre of Mass and Rotational Motion

Question

A circular hole of radius $$\left( {{a \over 2}} \right)$$ 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 :

Accepted Answer

Let $$\sigma$$ is the surface mass density of disc.
$${X_{com}} = {{(\sigma  	imes \pi {a^2} 	imes a) - (\sigma {{\pi {a^2}} \over 4} 	imes {{3a} \over 2})} \over {\sigma \pi {a^2} - {{\sigma \pi {a^2}} \over 4}}}$$
$$ \Rightarrow $$ $${X_{com}} = {{a - 3{a \over 8}} \over {1 - {1 \over 4}}}$$
$$ \Rightarrow $$ $${X_{com}} = {{{{5a} \over 8}} \over {{3 \over 4}}}$$
$$ \Rightarrow $$ $${X_{com}} = {{5a} \over 6}$$

Answer

$${1 \over 6}a$$

Answer

$${2 \over 3}a$$

Answer

$${5 \over 6}a$$

Answer

$${10 \over 11}a$$

Centre of Mass and Rotational Motion

A circular hole of radius $\left( {{a \over 2}} \right)$ 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 :

Choose the correct answer: