Question

A small solid sphere of mass $m$ and radius $r$ starting from rest from the rim of a fixed hemispherical bowl of radius $R(>>r)$ rolls inside it without sliding. The normal reaction exerted by the sphere on the hemisphere when it ,reaches the bottom of hemisphere is

• A. $\left(3/7\right)mg$
• B. $\left(9/7\right)mg$
• C. $\left(13/7\right)mg$
• D. $\left(17/7\right)mg$

Answer 1

The correct option is D $\left(17/7\right)mg$

At bottom total kinetic energy $=$ decrease in potential energy
$=mgR$ The ratio,$\frac{K_R}{K_r}=\frac{2}{5}$
$\therefore K_T=\frac{1}{2}m{v}^2=\frac{5}{7}mgR$
$\therefore \frac{m{v}^2}{R}=\frac{10}{7}mg=N-mg$
$\therefore N=\frac{17}{7}mg$