Mechanical Properties Of Fluids

Question

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64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

8 ms^-1

16 ms^-1

24 ms^-1

32 ms^-1

Solution

24 ms^-1

Volume of big drop = 64 x volume of a small drop

$\Rightarrow \frac{4}{3} π R^{3} = 64 \times \frac{4}{3} {πr}^{3}$

⇒ R = 4 r

The terminal velocity of spherical rain drop

$ν = \frac{2 r^{2} (ρ - σ)}{9 η}$

⇒ v ∝ r²

$\frac{v_{1}}{v_{2}} = {(\frac{r}{R})}^{2} = {(\frac{1}{4})}^{2}$

$\frac{v_{1}}{v_{2}} = \frac{1}{16}$

∴ v₂ = 16 v₁

= 16 × 1.5

v₂ = 24 ms^-1

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Mechanical Properties Of Fluids

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

8 ms^-1

16 ms^-1

24 ms^-1

32 ms^-1

Some More Questions From Mechanical Properties of Fluids Chapter

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

If two soap bubbles of different radii are connected by a tube,

A steam of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by

A wide hose pipe is held horizontally by a fireman. It delivers water through a nozzle at one litre per second. On increasing the pressure. this increases to two litres per second. The firman has now to

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Mechanical Properties Of Fluids

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is 8 ms-1 16 ms-1 24 ms-1 32 ms-1

Some More Questions From Mechanical Properties of Fluids Chapter

A jar filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3, is dropped in the jar. It comes to equilibrium in the position shown in the figure.Which of the following is true for ρ1, ρ2 and ρ3?

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution.Which of the following shows the relative nature of the liquid columns in the two tubes?

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

If two soap bubbles of different radii are connected by a tube,

A steam of a liquid of density ρ flowing horizontally with speed v rushes out of a tube of radius r and hits a vertical wall nearly normally. Assuming that the liquid does not rebound from the wall, the force exerted on the wall by the impact of the liquid is given by

A wide hose pipe is held horizontally by a fireman. It delivers water through a nozzle at one litre per second. On increasing the pressure. this increases to two litres per second. The firman has now to

A liquid is allowed into a tube of truncated cone shape. Identify the correct statement from the following.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

64 spherical rain drops of equal size are falling vertically through air with a terminal velocity 1.5 ms^-1 .If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is

8 ms^-1

16 ms^-1

24 ms^-1

32 ms^-1

A jar filled with two non-mixing liquids 1 and 2 having densities ρ₁ and ρ₂ respectively. A solid ball, made of a material of density ρ₃, is dropped in the jar. It comes to equilibrium in the position shown in the figure.
Which of the following is true for ρ₁, ρ₂ and ρ₃?