First slide

Methods to locate centre of mass

Question

Two semicircular rings of linear mass density $λ$ and $2 λ$ and of radius R are joined to form a complete ring. The distance of the center of mass of the complete ring from its centre is

Easy

A

$\frac{3 R}{8 π}$
B

$\frac{2 R}{3 π}$
C

$\frac{4 R}{21 π}$
D

None of these

Solution

$C_{1} (\frac{2 R}{π}, 0)$
$C_{2} (- \frac{2 R}{π}, 0)$
X – Co-ordinate of COM of the system
$= \frac{m (- 2 R / π) + 2 m (2 R / π)}{3 m} = \frac{2 R}{3 π}$

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