A spherical ballof radius 3-0-10-4m and density 104 kg-m3 falls freely under gravity through a distance h it before entering a tank of water coefficient of viscosity - - - 9-8 - 10-6 Nsm-2 and density - 103 kg-m3- If after entering the water- the velocity of the ball does not change- find h-Take g -9-8 ms-2

Terminal velocity, nbsp; u= √(2gh) = 2r^2(ρ σ)g/9η ⇒ h= 2gr^4(ρ r)^2/81 η^2= 1.65 km ...

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Standard XII

Physics

Terminal Velocity

A spherical b...

Question

A spherical ballof radius $3.0 \times 10^{- 4} m$ and density $10^{4}$ $k g / m^{3}$ falls freely under gravity through a distance h it before entering a tank of water (coefficient of viscosity = $η$ = $9.8 \times 10^{- 6} N s m^{- 2}$ and density = $10^{3} k g / m^{3}$ . If after entering the water, the velocity of the ball does not change, find~h.(Take g =9.8 $m s^{- 2}$ )

10.24 m

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1.65 km

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32.36 m

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50.12 m

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Solution

The correct option is B 1.65 km
Terminal velocity,
$u = \sqrt{2 g h} = \frac{2 r^{2} (ρ - σ) g}{9 η} \Rightarrow h = \frac{2 g r^{4} (ρ - r)^{2}}{81 η^{2}} = 1.65 k m$

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The correct option is B 1.65 kmTerminal velocity, u=√2gh=2r2(ρ−σ)g9η⇒h=2gr4(ρ−r)281η2=1.65km

The correct option is B 1.65 km
Terminal velocity,
$u = \sqrt{2 g h} = \frac{2 r^{2} (ρ - σ) g}{9 η} \Rightarrow h = \frac{2 g r^{4} (ρ - r)^{2}}{81 η^{2}} = 1.65 k m$