Question

A hollow hemisphere of mass $4m$ is placed as shown in figure. Two point masses $m$ each are fixed to it at points $P$ and $Q$ on diametrically opposite points. The position of center of mass of the system is

• A. $\left(0 , - \frac{R}{2}\right)$
• B. $\left(0 , - \frac{R}{3}\right)$
• C. $\left(0 , - \frac{2 R}{3}\right)$
• D. $\left(0 , - \frac{R}{4}\right)$

Answer 1

Answer: (B)

Centre of mass for cut portion from a body
$X_{c m}=\frac{m_{1} \, x_{1} - m_{2} \, x_{2}}{m_{1} + m_{2}}$
$X_{c m}=\frac{m R - m R}{6 m}=0$
$Y_{c m}=\frac{4 m \times \left(\frac{- R}{2}\right)}{6 m}=- \, R / 3$