Question

A ball of mass $m$ and radius $r$ rolls inside a hemispherical shell of radius $R$. It is released from rest from point A as shown if figure. The normal force between the ball and the shell in position B is

• A. $\frac{12}{7}mg$
• B. $\frac{7}{9}mg$
• C. $\frac{17}{7}mg$
• D. $\frac{10}{7}mg$

Answer 1

The correct option is C $\frac{17}{7}mg$

From geometry, $OA=R-r$

Work-energy theorem, $mg(R-r)=\frac{1}{2}I{w}^2+\frac{1}{2}m{v}^2$

$mg(R-r)=\frac{1}{2}\times \frac{2}{5}m{r}^2{w}^2+\frac{1}{2}m{v}^2$ $(v=rw)$

$⟹mg(R-r)=\frac{7}{10}m{v}^2$

Also, circular motion equation: $\frac{m{v}^2}{R-r}=N-mg$

$\frac{10}{7}mg=N-mg⟹N=\frac{17}{7}mg$