Question

A small ball of mass $m$ and radius $r$ rolls inside a hemispherical shell of radius $R$ as shown if figure. The angular velocity of centre of the ball in position $2$ about the centre of the shell is

• A. $2\sqrt{\frac{g}{5(R-r)}}$
• B. $\sqrt{\frac{10g}{7(R-r)}}$
• C. $\sqrt{\frac{2g}{5(R-r)}}$
• D. $\sqrt{\frac{5g}{2(R-r)}}$

Answer 1

Answer: (B)

$\sqrt{\frac{10g}{7(R-r)}}$

$usingconservationofenergymg(R-r)=\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^{2}v=\omega r,I=\frac{2}{5}m{r}^{2}mg(R-r)=\frac{1}{2}m{v}^2+\frac{1}{2}\times \frac{2}{5}m{r}^2\times {\omega }^2=\frac{7}{10}m{v}^{2}v=\sqrt{\frac{10g(R-r)}{7}},angularvelocityaboutthecenter\Omega =\frac{v}{R-r}=\sqrt{\frac{10g}{7(R-r)}}$