Question

A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of masses 2 kg each are placed at the interesting points of the circle with +ve x-axis and +ve y-axis. Then , the angle made by the position vector of centre of mass of entire system with x-axis is :

• A. ${45}^0$
• B. ${60}^0$
• C. ${\tan }^{-1}\left(\frac{4}{5}\right)$
• D. ${30}^0$

Answer 1

The correct option is A ${45}^0$

Ring has center of mass at $(0,0)$

the particle on +x axis will be at $(a,0)$

the particle on +y axis will be at $(0,a)$

so the center of mass will be at $x=\frac{6\times 0+2\times a+2\times 0}{6kg+2kg+2kg}=\frac{a}{5}$

and $y=\frac{6\times 0+2\times 0+2\times a}{6kg+2kg+2kg}=\frac{a}{5}$

the angle with x axis will be $ta{n}^{-1}\frac{y}{x}={45}^0$