First slide

Conservation of mechanical energy

Question

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

Moderate

A

$\sqrt{2 g h}$
B

$\sqrt{2 g R}$
C

$\sqrt{2 g (R + h)}$
D

$\sqrt{2 g (R - h)}$

Solution

From the principle of conservation of energy, we have
$\frac{1}{2} {mv}^{2} + mgh = 0 + mgR$
which gives $v = \sqrt{2 g (R - h)}$ . Hence the correct choice is (d).

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