Question

A circular ring of mass $6\text{kg}$ and radius $a$ is placed such that its centre at the origin. Two particles of masses $2\text{kg}$ each are placed at the intersecting points of the circle with positive x-axis and positive y-axis. Then, the angle made by the position vector of centre of mass of entire system with x-axis is

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${\tan }^{-1}\left(\frac{4}{5}\right)$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${45}^{\circ }$


$X_{cm}$ be x- coordinate of COM of system of particles
$Y_{cm}$ be y- coordinate of COM of system of particles
Then angle made by COM of position vector with x-axis is
$\tan \theta =\frac{Y_{cm}}{X_{cm}}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3}{m_1{x}_1+m_2{x}_2+m_3{x}_3}=\frac{6\times 0+2\times 0+2\times a}{6\times 0+2\times a+2\times 0}=1$

$\theta ={45}^{\circ }$