Question

From a solid sphere of radius 2 m a sphere of radius 1 m is removed. The new centre of mass from $C_1$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

At $c_1$ mass of the whole surface can be imagined.

At $c_2$ mass of the removed sphere can be imagined.

$\therefore$ $x_{cm}$ = $\frac{V_1{x}_1+V_2{x}_2}{V_1+V_2}$

$x_{cm}=\frac{\frac{4}{3}\pi r_1^3\left(0\right)-\frac{4}{3}\pi r_2^3(1{)}^3}{\frac{4}{3}\pi r_1^3-\frac{4}{3}\pi r_2^3}=-\frac{r_2^3}{r_1^3-r_2^3}=\frac{-1}{8-1}=\frac{-1}{7}m$

$\therefore$ The new centre of mass is \frac 17 m from $C_1$ towards left.