Question

A small ball is pushed from a height h along a smooth hemispherical bowl of radius R. With what speed should the ball be pushed so that it just reaches the top of the opposite end of the bowl?

• A. $\sqrt{2gh}$
• B. $\sqrt{2}gh(R+h)$
• C. $\sqrt{2}g(R-h)$
• D. None of these

Answer 1

The correct option is C $\sqrt{2}g(R-h)$

when the ball $n$ at height $h$ the $P.E_1$ of the ball in $mgh$

when the ball is pushed with velocity $v$ it reaches

The bottom with $K.E_1=\frac{1}{2}m{v}^2$

Thus by inertia the ball Travel upto $R$ when its

$P.E_2=mgRandvelocity=0$

$K.E_2=0$

$\therefore$ From low of conservation of energy

$P{E}_1+K{E}_1=P{E}_2+K{E}_2$

$mgh+\frac{1}{2}m{v}^2=mgR+0$

so $\therefore v=\sqrt{2g(R-h)}$