A spherical ballof radius 3.0 × 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 × 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 ) Options: A . &nbsp 10.24 m B . &nbsp 1.65 km C . &nbsp 32.36 m D . &nbsp 50.12 m

Answer: Option B : B Terminal velocity, u = √ 2 g h = 2 r 2 ( ρ − σ ) g 9 η ⇒ h = 2 g r 4 ( ρ − r ) 2 81 η 2 = 1.65 k m

A spherical ballof radius 3.0×10−4m and density 104 kg/m

Discussion Forum : Mechanical Properties Of Fluids

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 $m s^{- 2}$ )

Options:

A . 10.24 m

B . 1.65 km

C . 32.36 m

D . 50.12 m

Answer: Option B
:
B

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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Discussion Forum : Mechanical Properties Of Fluids

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