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

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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-qxptiutlgobm.png" /> (A) (0 , - (R/2)) (B) (0 , - (R/3)) (C) (0 , - (2 R/3)) (D) (0 , - (R/4))

Tardigrade Admin · Accepted Answer

Centre of mass for cut portion from a body Xc m=(m1 x1 - m2 x2/m1 + m2) Xc m=(m R - m R/6 m)=0 Yc m=(4 m × ((- R/2))/6 m)=- R / 3

Q. A hollow hemisphere of mass $4 m$ 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

$(0, - \frac{R}{2})$

$(0, - \frac{R}{3})$

$(0, - \frac{2 R}{3})$

$(0, - \frac{R}{4})$

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

Q. 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

(0,−2R​)

(0,−3R​)

(0,−32R​)

(0,−4R​)