A body of 200g begins to fall from a height where its potential energy is 80 J. Its velocity at a point where kinetic and potential energies are equal is

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20 m/s

10 $\sqrt{8}$ m / s

4 m/s

400 m/s

answer is D.

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Detailed Solution

$h = \frac{80}{0.2 \times 10} = \frac{80}{2} = 40 m$
given, PE = KE

$\Rightarrow mg (h - x) = \frac{1}{2} m (2 gx)$
$mgh - mgx = mgx \Rightarrow mgh = 2 mgx$
$x = h / 2$
$v = \sqrt{2 gx} = \sqrt{2 \times 10 \times 20} = 20 m / s$

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