A metallic sphere of radius 1x10^-3m and density 1x10⁴ kg / m³ enters a tank of water, after a free tall through a distance of ‘h’ in earth’s gravitational field . If its velocity remains unchanged after entering water, determine the value of ‘h’ (in m). (Given coefficient of viscosity = 1.0 x 10^-3N - s / m² and density of water = 1.0 x 10³kg / m³ )

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answer is 20.

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Detailed Solution

The velocity attained by the sphere in falling freely from a height 'h' is $V = \sqrt{2 gh} \to (1)$
This is the terminal velocity of the sphere in water hence by stroke’s law, we have
$V = \frac{2}{9} r^{2} \frac{(ρ - σ)}{η} . . . . . . . . (2)$

$\Rightarrow \sqrt{2 \times 10 \times h} = \frac{2 \times {(1 \times 10^{- 3})}^{2} (1 \times 10^{4} - 1 \times 10^{3}) \times 10}{9 \times 1 \times 10^{- 3}} = 20$