Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2 respectively. The rate of flow will be ____ cm3/s. (take g = 10 m/s2)

### Related Formula ### Core Logic From the continuity equation between A and B: Applying Bernoulli's equation between A and B for a horizontal pipe: Since the height difference is h = 5 cm = 0.05 m, the pressure difference is gh. ### Step 1: Calculate Velocity and Volume Flow Rate Solving for VA: Volume flow rate Q = AA VA: ### Pattern Recognition In a horizontal Venturi meter, substituting V2 = V1 (A1/A2) directly into g h = (1/2) (V22 - V12) is the standard path. Working in CGS vs MKS units requires careful tracking; convert VA to cm/s before multiplying by AA in cm². ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Mechanical Properties of Fluids

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2

### Related Formula ### Core Logic From the continuity equation between A and B: Applying Bernoulli's equation between A and B for a horizontal pipe: Since the height difference is h = 5 cm = 0.05 m, the pressure difference is gh. ### Step 1: Calculate Velocity and Volume Flow Rate Solving for VA: Volume flow rate Q = AA VA: ### Pattern Recognition In a horizontal Venturi meter, substituting V2 = V1 (A1/A2) directly into g h = (1/2) (V22 - V12) is the standard path. Working in CGS vs MKS units r

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2 respectively. The rate of flow will be ____ cm3/s. (take g = 10 m/s2)

### Related Formula ### Core Logic From the continuity equation between A and B: Applying Bernoulli's equation between A and B for a horizontal pipe: Since the height difference is h = 5 cm = 0.05 m, the pressure difference is gh. ### Step 1: Calculate Velocity and Volume Flow Rate Solving for VA: Volume flow rate Q = AA VA: ### Pattern Recognition In a horizontal Venturi meter, substituting V2 = V1 (A1/A2) directly into g h = (1/2) (V22 - V12) is the standard path. Working in CGS vs MKS units requires careful tracking; convert VA to cm/s before multiplying by AA in cm². ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Mechanical Properties of Fluids

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm2 and 3 cm2

### Related Formula ### Core Logic From the continuity equation between A and B: Applying Bernoulli's equation between A and B for a horizontal pipe: Since the height difference is h = 5 cm = 0.05 m, the pressure difference is gh. ### Step 1: Calculate Velocity and Volume Flow Rate Solving for VA: Volume flow rate Q = AA VA: ### Pattern Recognition In a horizontal Venturi meter, substituting V2 = V1 (A1/A2) directly into g h = (1/2) (V22 - V12) is the standard path. Working in CGS vs MKS units r

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in…

Year	2026	2025	2024	Total
Questions	9	15	8	32

Year

2026

2025

2024

Total

Questions

Solution & Explanation

Related Formula

A₁ V₁ = A₂ V₂

P₁ + (1)/(2)ρ V₁² = P₂ + (1)/(2)ρ V₂²

P₁ - P₂ = ρ g h

Core Logic

From the continuity equation between A and B:

AAVA = ABVB 6VA = 3VB VB = 2VA

Applying Bernoulli's equation between A and B for a horizontal pipe:

PA + (1)/(2)ρ VA² = PB + (1)/(2)ρ VB²

PA - PB = (1)/(2)ρ(VB² - VA²)

Since the height difference is $h = 5 cm = 0.05 m$ $h = 5\text{ cm} = 0.05\text{ m}$, the pressure difference is $ρ gh$ $\rho gh$.

ρ g \times 0.05 = (1)/(2)ρ( (2VA)² - VA² )

g \times 0.05 = (1)/(2)(3VA²)

Step 1: Calculate Velocity and Volume Flow Rate

Solving for $VA$ $V_A$:

VA = \sqrt((2 \times 10 \times 0.05)/(3)) = \sqrt((1)/(3)) = 1\sqrt(3) m/s

VA = 100\sqrt(3) cm/s

Volume flow rate $Q = AA VA$ $Q = A_{A} V_{A}$:

Q = 6 cm² \times 100\sqrt(3) cm/s = 600\sqrt(3) = 200\sqrt(3) cm³/s

Pattern Recognition

In a horizontal Venturi meter, substituting $V₂ = V₁ (A₁/A₂)$ $V_2 = V_1 (A_1/A_2)$ directly into $ρ g h = (1)/(2)ρ (V₂² - V₁²)$ is the standard path. Working in CGS vs MKS units requires careful tracking; convert $VA$ $V_A$ to cm/s before multiplying by $AA$ $A_A$ in cm².

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

More Mechanical Properties of Fluids Previous-Year Questions

Q38 jee_main_2026_21_jan_evening Surface Tension

Surface tension of two liquids (having same densities),

T₁

and

T₂

, are measured using capillary rise method utilizing two tubes with inner radii of

r₁

and

r₂

where

r₁ > r₂

. The measured liquid heights in these tubes are

h₁

and

h₂

respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights

h₁

and

h₂

and surface tensions

T₁

and

T₂

satisfy the relation :

A. $h₁ < h₂ and T₁ = T₂$ $h_1 < h_2 \text{ and } T_1 = T_2$
B. $h₁ = h₂ and T₁ = T₂$ $h_1 = h_2 \text{ and } T_1 = T_2$
C. $h₁ > h₂ and T₁ = T₂$ $h_1 > h_2 \text{ and } T_1 = T_2$
D. $h₁ > h₂ and T₁ < T₂$ $h_1 > h_2 \text{ and } T_1 < T_2$

Solution

Related Formula

h = (2T θ)/(ρ g r)

Core Logic

Since we are assessing surface tension $T$ $T$ as a property of the liquids, the question intends to compare liquids that are identical (implying $T₁ = T₂$ $T_1 = T_2$ and same density).

Capillary rise formula block for Q38 - JEE Main 2026 Evening

By Jurin's Law, for identical liquids, the height of capillary rise is inversely proportional to the radius of the tube:

h \propto (1)/(r)

Step 1: Final Conclusion

Given $r₁ > r₂$ $r_1 > r_2$, the inverse proportionality directly implies that the liquid will rise less in the wider tube. Therefore, $h₁ < h₂$ $h_1 < h_2$ and naturally $T₁ = T₂$ $T_1 = T_2$ for the intrinsic property.

Pattern Recognition

Wider tubes ( $r$ $r$ large) cause lower capillary rises ( $h$ $h$ small). $h \propto 1/r$ $h \propto 1/r$ is a foundational inverse relationship in capillary action.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Q47 jee_main_2026_21_jan_evening Terminal Velocity

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.

Numerical Answer. Answer: 5 to 5

Solution

Related Formula

vT = (2r² g)/(9η) (σ - ρ)

Core Logic

For balls of the same material falling through the same fluid, all terms in the terminal velocity equation except the radius $r$ $r$ are constant. Therefore, $vT \propto r²$ $v_T \propto r^2$.

Step 1: Setting up the Ratio

((vT)₁)/((vT)₂) = ((r₁)/(r₂))²

Substituting the given values: $r₁ = 6 mm$ $r_1 = 6 \text{ mm}$, $(vT)₁ = 20 cm/s$ $(v_T)_1 = 20 \text{ cm/s}$ $r₂ = 3 mm$ $r_2 = 3 \text{ mm}$

Step 2: Final Conclusion

(20)/((vT)₂) = ((6)/(3))²

(20)/((vT)₂) = 2² = 4

(vT)₂ = (20)/(4) = 5 cm/s

Pattern Recognition

Terminal velocity is directly proportional to the square of the radius. Halving the radius ( $6 \to 3$ $6 \to 3$) will drop the terminal velocity by a factor of $1/4$ $1/4$.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Q33 jee_main_2026_22_january_morning Pascal's Law and Surface Tension

Given below are two statements: Statement I : Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. In the light of the above statements, choose the correct answer from the options given below:

A. $Statement I is true but Statement II is false$
B. $Both Statement I and Statement II are false$
C. $Both Statement I and Statement II are true$
D. $Statement I is false but Statement II is true$

Solution

Related Formula

P = (F)/(A), Surface Tension \propto Δ U

Core Logic

According to Pascal's law, pressure exists at every point in a liquid at rest, not just at boundaries. Thus, Statement I is false.

For interior molecules, net cohesive forces are zero, whereas surface molecules possess excess potential energy leading to surface tension. Thus, Statement II is correct.

Pattern Recognition

Sees: Fluid pressure definition + surface tension origin. Shortcut: Recall Pascal's law (pressure everywhere) and surface energy excess. Check: Matches option (4). ✓

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Q34 jee_main_2026_22_january_evening Capillarity and Surface Tension

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises up to certain height h. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by 1 % each, then the height of the liquid in the tube will change by ____%.

A. $-1$ $-1$
B. $+3$ $+3$
C. $-3$ $-3$
D. $+1$ $+1$

Solution

Related Formula

h = (2T θ)/(ρ g r)

(Δ h)/(h)% = (Δ T)/(T)% - (Δ ρ)/(ρ)% - (Δ r)/(r)%

Core Logic

Applying fractional error analysis to the capillary rise formula:

(Δ h)/(h)% = (-1%) - (-1%) - (-1%)

(Δ h)/(h)% = -1 + 1 + 1 = +1%

Capillary tube rise calculation diagram for Q34 - JEE Main 2026 Evening

Step 1: Final Conclusion

The height of the liquid in the tube increases by $+1%$ $+1\%$.

Pattern Recognition

Percentage error in capillary rise: $h \propto (T)/(ρ r)$ $h \propto \frac{T}{\rho r}$. Decreasing numerator $T$ $T$ by 1% reduces $h$ $h$ by 1% ( $-1%$ $-1\%$). Decreasing denominators $ρ$ $\rho$ and $r$ $r$ by 1% each increases $h$ $h$ by 1% twice ( $+1% + 1%$ $+1\% + 1\%$). Net change: $-1 + 1 + 1 = +1%$ $-1 + 1 + 1 = +1\%$.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Solution & Explanation

Related Formula

Core Logic

Step 1: Calculate Velocity and Volume Flow Rate

Pattern Recognition

Chapter Mix

More Mechanical Properties of Fluids Previous-Year Questions

Solution

Related Formula

Core Logic

Step 1: Final Conclusion

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Setting up the Ratio

Step 2: Final Conclusion

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Pattern Recognition

Chapter Mix

Solution

Related Formula

Core Logic

Step 1: Final Conclusion

Pattern Recognition

Chapter Mix

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