Question

A semi circular ring of radius $2\pi$ is situated in $X-Y$ plane having centre at $(10,10)$ as shown in the figure below. Find the co-ordinates of centre of mass of the ring.

• A. $(12,10)$
• B. $(10,14)$
• C. $(14,14)$
• D. $(10,10)$

Answer 1

The correct option is B $(10,14)$

The given ring is symmetric about line $X=10$, therefore, the $COM$ of this ring will lie on the line $X=10$, hence $X-$ co-ordinate of $COM$ will be $10$.


And we know, distance of $COM$ of a semicircle from its centre is $h=\frac{2R}{\pi }$, and radius of ring is $2\pi$.
Therefore, position of $COM$ from centre will be $h=\frac{2\times 2\pi }{\pi }=4$
i.e $Y-$ co-ordinate of $COM$ will be $h+10=14$

Hence coordinates of $COM$ will be $(10,14)$.