Question

Two discs of radii 4 cm and 2 cm respectively are attached as shown in the figure. The new centre of mass of the system from '$C_1$' is

• A. 1 cm
• B. 1.2 cm
• C. 1.3 cm
• D. 1.4 cm

Answer 1

The correct option is B

1.2 cm

$x_{cm}$ = $\frac{m_1\left(0\right)+m_2\left(6\right)}{m_1+m_2}$

As, surface density $\sigma =\frac{m}{A}\Rightarrow m=\sigma A$

$\Rightarrow x_{cm}=\frac{\sigma A_2\left(6\right)}{\sigma A_1+\sigma A_2}=\frac{6\pi r_2^2}{\pi (r_1^2+r_2^2)}$

$\Rightarrow x_{cm}=\frac{6(2{)}^2}{4^2+2^2}=1.2cm$