First slide

Viscosity

Question

A streamlined body falls through air from a height h on the surface of a liquid. If d and D (> d) represent the densities of the material of the body and liquid respectively, then the
time after which the body will be instantaneously at rest, is:

Difficult

A

$\sqrt{\frac{2 h}{g}}$
B

$\sqrt{\frac{2 h}{g}} \frac{D}{d}$
C

$\sqrt{\frac{2 h}{g} \frac{D}{d}}$
D

$\sqrt{\frac{2 h}{g}} (\frac{d}{D - d})$

Solution

When body enter in water then velocity $= \sqrt{2 gh}$
Retardation on body $= a = \frac{Th - W}{m} = g (\frac{D - d}{d})$
Time at which the body will be at rest
$t = \frac{v}{a} = \frac{\sqrt{2 gh}}{g (\frac{D - d}{d})} = \sqrt{\frac{2 h}{g}} (\frac{d}{D - d})$

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