Question

A hemispherical cavity of radius $R$ is created in a solid sphere of radius $2R$ as shown in the figure. The $y$ -coordinate of the centre of mass of the remaining sphere is

• A. $y_{CM}=-\frac{R}{15}$
• B. $y_{CM}=-\frac{R}{40}$
• C. $y_{CM}=-\frac{R}{30}$
• D. $y_{CM}=-\frac{R}{20}$

Answer 1

Answer: (B)

$x _{ CM }=\frac{\frac{4}{3} \pi(2 R )^{3} 0-\frac{2}{3} \pi R ^{3} R }{\frac{4}{3} \pi(2 R )^{3}-\frac{2}{3} \pi R ^{3}}=-\frac{ R }{15}$
$y _{ CM }=\frac{\frac{4}{3} \pi(2 R )^{3} 0-\frac{2}{3} \pi R ^{3} \frac{3 R }{8}}{\frac{4}{3} \pi(2 R )^{3}-\frac{2}{3} \pi R ^{3}}=-\frac{ R }{40}$