Fluid Mechanics | Surface Tension And Viscosity | JEE Main previous year questions with Solutions

Q 11 :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: A spherical body of radius $(5 \pm 0.1)$ mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%.

Reason R: The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

In the light of the above statements, choose the correct answer from the options given below [2023]

Both A and R are true but R is NOT the correct explanation of A
Both A and R are true and R is the correct explanation of A
A is false but R is true
A is true but R is false

1

2

3

4

(4)

$Terminal velocity of a spherical body in liquid$

$\Rightarrow V_{t} \propto r^{2} \Rightarrow \frac{Δ V_{t}}{V_{t}} = 2 \cdot \frac{Δ r}{r}$

$\Rightarrow \frac{Δ V_{t}}{V_{t}} \times 100 % = 2 \frac{0.1}{5} \times 100 = 4 %$

$Also V_{t} \propto r^{2}$

$Reason R is false$

Q 12 :

A spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. The viscous force on the ball when it attains constant velocity is $3696 \times 10^{- x} N$ . The value of $x$ is. (Given: $g = 9.8 {m/s}^{2}$ and $π = \frac{22}{7}$ ) ________ . [2023]

0%

(7)

$When the ball attains terminal velocity$

$F_{v} = (m g - F_{B}) (∵ a = 0)$

$= V σ_{b} g - V ρ_{ℓ} g = V (σ_{b} - ρ_{ℓ})$

$= \frac{4}{3} π {(10^{- 3})}^{3} \times 9.8 (10.5 - 1.5) \times 10^{3}$

$= 3696 \times 10^{- 7} N$

$So, x = 7$

Q 13 :

A metal block of base area $0.20 m^{2}$ is placed on a table, as shown in the figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is $5.0 \times 10^{- 3}$ poiseuille, the speed of the block is _______ $\times 10^{- 3} m/s$ . [2023]

0%

(25)

$| F |$ $= η A \frac{Δ v}{Δ h}$ : $0.1 = 5 \times 10^{- 3} \times 0.2 \times \frac{v}{0.25 \times 10^{- 3}}$

$v = 0.025 m/s or v = 25 \times 10^{- 3} m/s$

Q 14 :

An air bubble of diameter 6 mm rises steadily through a solution of density $1750 {kg/m}^{3}$ at the rate of 0.35 cm/s. The coefficient of viscosity of the solution (neglect density of air) is _______ P as (given, $g = 10 {ms}^{- 2}$ ). [2023]

0%

(10)

Since the bubble is moving at constant speed, the force acting on it is zero.

$B = F_{v}$

$\frac{4}{3} π R^{3} ρ g = 6 π η R v$

$η = \frac{2 R^{2} ρ g}{9 v} = \frac{2 \times {(3 \times 10^{- 3})}^{2} \times 1750 \times 10}{9 \times 0.35 \times 10^{- 2}} = 10 Pas$

Q 15 :

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of the bigger drop is ______ cm/s. [2026]

0%

(160)

$V_{T} = \frac{2 r^{2} g}{9 η} (σ - ρ)$

$V_{T} \propto r^{2}$

$64 drops$

$64 (\frac{4}{3} π R_{1}^{3}) = \frac{4}{3} π R_{2}^{3}$

$R_{2} = 4 R_{1}$

$\frac{{(V_{T})}_{1}}{{(V_{T})}_{2}} = {(\frac{R_{1}}{R_{2}})}^{2} = {(\frac{1}{4})}^{2}$

$\frac{10}{{(V_{T})}_{2}} = \frac{1}{16}$

${(V_{T})}_{2} = 160 cm/sec$

Q 16 :

A small metallic sphere of diameter 2 mm and density $10.5 {g/cm}^{3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5 {g/cm}^{3}$ respectively. The terminal velocity attained by the sphere is ____ cm/s.

$(π = \frac{22}{7} and g = 10 {m/s}^{2})$ [2026]

3.0
1.0
2.0
1.5

1

2

3

4

(3)

$V_{T} = \frac{2 r^{2} g}{9 η} (ρ_{b} - ρ_{ℓ})$

$V_{T} = \frac{2}{9} \cdot \frac{{(1)}^{2} \times 10}{10} (10.5 - 1.5)$

$V_{T} = 2 cm/sec.$

Q 17 :

A ball of radius r and density $ρ$ dropped through a viscous liquid of density $σ$ and viscosity $η$ attains its terminal velocity at time t, given by $t = A ρ^{a} r^{b} η^{c} σ^{d}$ where A is a constant and a,b,c and d are integers. The value of $\frac{b + c}{a + d} is$ _______. [2026]

0%

(1)

$T = {(M L^{- 3})}^{a} L^{b} {(M L^{- 1} T^{- 1})}^{c} (M L^{- 3})^{d}$

$T = M^{a + c + d} L^{- 3 a - c - 3 d + b} T^{- c}$

$on comparing$

$c = - 1; a + c + d = 0; - 3 a - c - 3 d + b = 0$

$b = 2; a + d = 1$

$b + c = 1$

Q 18 :

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm, in the same fluid will be ______ cm/s. [2026]

0%

(5)

$We know:$

$Terminal velocity \propto {(radius)}^{2}$

$\frac{{(v_{T})}_{1}}{{(v_{T})}_{2}} = {(\frac{6}{3})}^{2}$

${(v_{T})}_{2} = \frac{{(v_{T})}_{1}}{4} = 5 cm/sec$

Topic Question Set

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Q 14 :

An air bubble of diameter 6 mm rises steadily through a solution of density $1750 {kg/m}^{3}$ at the rate of 0.35 cm/s. The coefficient of viscosity of the solution (neglect density of air) is _______ P as (given, $g = 10 {ms}^{- 2}$ ). [2023]

0%

Q 15 :

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of the bigger drop is ______ cm/s. [2026]

0%

Q 16 :

A small metallic sphere of diameter 2 mm and density $10.5 {g/cm}^{3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5 {g/cm}^{3}$ respectively. The terminal velocity attained by the sphere is ____ cm/s.

$(π = \frac{22}{7} and g = 10 {m/s}^{2})$ [2026]

0%

Q 18 :

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm, in the same fluid will be ______ cm/s. [2026]

0%

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Topic Question Set

Q 12 : A spherical ball of radius 1 mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. The viscous force on the ball when it attains constant velocity is 3696×10-x N. The value of x is. (Given: g=9.8 m/s2 and π=227) ________ . [2023]

0%

0%

Q 14 : An air bubble of diameter 6 mm rises steadily through a solution of density 1750 kg/m3 at the rate of 0.35 cm/s. The coefficient of viscosity of the solution (neglect density of air) is _______ P as (given, g=10 ms-2). [2023]

0%

Q 15 : Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of the bigger drop is ______ cm/s. [2026]

0%

Q 16 : A small metallic sphere of diameter 2 mm and density 10.5 g/cm3 is dropped in glycerine having viscosity 10 Poise and density 1.5 g/cm3 respectively. The terminal velocity attained by the sphere is ____ cm/s. (π=227 and g=10 m/s2) [2026]

Q 17 : A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by t=A ρarbηcσd where A is a constant and a,b,c and d are integers. The value of b+ca+d is _______. [2026]

0%

Q 18 : The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm, in the same fluid will be ______ cm/s. [2026]

0%

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Q 14 :

An air bubble of diameter 6 mm rises steadily through a solution of density $1750 {kg/m}^{3}$ at the rate of 0.35 cm/s. The coefficient of viscosity of the solution (neglect density of air) is _______ P as (given, $g = 10 {ms}^{- 2}$ ). [2023]

Q 15 :

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of the bigger drop is ______ cm/s. [2026]

Q 16 :

A small metallic sphere of diameter 2 mm and density $10.5 {g/cm}^{3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5 {g/cm}^{3}$ respectively. The terminal velocity attained by the sphere is ____ cm/s.

$(π = \frac{22}{7} and g = 10 {m/s}^{2})$ [2026]

Q 18 :

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm, in the same fluid will be ______ cm/s. [2026]