Question

You are supplied with three identical rods of same length and mass . If the length of each rod is $2\pi$. Two of them are converted into rings and then placed over the third rod as shown in figure. If point A is considered as origin of the coordinates system, the coordinate of the centre of mass will be (you may assume AB as x - axis of the coordinate system)

• A. $(\frac{\pi }{2},\frac{1}{3})$
• B. $(\frac{\pi }{2},\frac{2}{3})$
• C. $(\pi ,\frac{1}{3})$
• D. $(\pi ,\frac{2}{3})$

Answer 1

The correct option is D $(\pi ,\frac{2}{3})$

$2\pi R=2\pi \therefore R=1$
$Y_{CM}=\frac{m\times 0+m\times 1+m\times 1}{m+m+m}=\frac{2}{3}$
$X_{CM}=\frac{m\left(\pi \right)+m\left(0\right)+m\left(2\pi \right)}{m+m+m}=\pi$