You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Freefall & Motion

A ball of rad...

Question

A ball of radius r and density Ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is h, the value of h is given by

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C
Velocity of ball when it strikes the water surface $v = \sqrt{2 g h} . . . (i)$

Terminal velocity of ball inside the water $v = \frac{2}{9} r^{2} g \frac{(ρ - 1)}{η} . . . . (i i)$

Equating (i) and (ii) we get $\sqrt{2 g h} = \frac{2}{9} \frac{r^{2} g}{η} (ρ - 1)$

$\Rightarrow h = \frac{2}{81} r^{4} {(\frac{ρ - 1}{η})}^{2} g$

Suggest Corrections

Similar questions

A ball of radius r and density $ρ$ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is n, the value of h is given by

Q. A small spherical ball of radius r falls freely under gravity through a distance h before entering a tank of water. If, after entering the water, the velocity of the ball does not change, then h is proportional

Q. A spherical of radius

3.0 \times 10^{- 4} m

and density

10^{4} K g / m^{3}

falls freely under the gravity through a distance

h

before entering a tank of water. If after entering the water the velocity of the balls does not change, Find

h

. Viscosity of water is

9.8 \times 10^{- 6} N - s / m^{2} . [g = 9.8 m / s^{2}]

Q. A spherical ball of radius

1 \times 10^{- 4} m

and density

10^{4} k g / m^{3}

falls freely under gravity through a distance

h

before entering a tank of water. If after entering the water the velocity of the ball does not change, find

h

in m (Write answer to nearest interger). (The viscosity of water is

9.8 \times 10^{- 6} {N - s / m}^{2}

)

Q. 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}

)

Join BYJU'S Learning Program

A ball of radius r and density Ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is h, the value of h is given by

The correct option is C Velocity of ball when it strikes the water surface v=√2gh ...(i) Terminal velocity of ball inside the water v=29r2 g(ρ−1)η ....(ii) Equating (i) and (ii) we get √2gh=29r2 gη(ρ−1) ⇒ h=281r4(ρ−1η)2 g