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Standard XII

Physics

Terminal Velocity

A metal ball ...

Question

A metal ball of radius $1 m m$ and density $10^{4}$ kg m $^{- 3}$ . falls freely in air through a height ' $h$ ' before falling in a tank full of water. If on falling in water its velocity remains unchanged, then the value of h will be (Coefficient of viscosity of water $= 10^{- 3}$ Pa.s and $g = 10 m s^{- 2}$ )

10 m

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15 m

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25 m

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20 m

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Solution

The correct option is D $20 m$
As the velocity of the ball remains unchanged in the water which implies that the ball reached its terminal velocity in water,(just before touching the water)
$V = \frac{2 r^{2} (T_{s} - T) g}{9 η} = \frac{2 (10^{- 3}) \times 10 \times (10^{4} - 10^{3})}{9 \times 10^{- 3}} = 20 m / s$
Neglecting the viscous effect of air,
We calculate the distance covered by the ball to reach the velocity of $20 m / s$
$V^{2} - V^{2} = 2 a S$
$\Rightarrow (20)^{2} = 2 \times 10 \times h$
$\Rightarrow \frac{400}{20} = h \Rightarrow h = 20 m .$

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A metal ball of radius 1mm and density 104kg m−3. falls freely in air through a height 'h' before falling in a tank full of water. If on falling in water its velocity remains unchanged, then the value of h will be (Coefficient of viscosity of water =10−3 Pa.s and g=10ms−2)