Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases. D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

Related Formula

Core Logic

Let us check each statement sequentially:

Statement A: Since VT ∝ R²$\mathrm{V}_{\mathrm{T}} \propto \mathrm{R}^2$, the graph between terminal velocity V$\mathrm{V}$ and radius R$\mathrm{R}$ is a quadratic curve, i.e., a parabola. (True)

Statement B: Different diameters imply different radii, hence terminal velocity will change. It is not constant. (False)

Statement C: Viscosity of a liquid is heavily temperature-dependent, hence VT$\mathrm{V}_{\mathrm{T}}$ changes with temperature. (True)

Statement D: Knowing the parameters allows calculation of liquid density ρ$\rho$. (True)

Statement E: η$\eta$ is a material property of the fluid and does not change based on the initial dropping speed of the ball. (False)

Step 1: Final Conclusion

Statements A, C, and D are correct, which matches option (2).

Pattern Recognition

Terminal velocity problems rely entirely on parsing the proportional relations hidden in Stokes' Law formulation. Note that viscosity coefficient is an intrinsic characteristic parameter independent of kinematics.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Related Formula

• Concave meniscus: θ < 90^° implies θ > 0$\theta < 90^\circ implies \cos\theta > 0$
• Convex meniscus: θ > 90^° implies θ < 0$\theta > 90^\circ implies \cos\theta < 0$

Core Logic

For K$K$ to be negative, θA$\cos\theta_{\mathrm{A}}$ and θB$\cos\theta_{\mathrm{B}}$ must have opposite mathematical signs.

Looking at option (3):

• Liquid A has a concave meniscus implies θA < 90^° implies θA > 0$implies \theta_{\mathrm{A}} < 90^\circ implies \cos\theta_{\mathrm{A}} > 0$ (positive).
• Liquid B has a convex meniscus implies θB > 90^° implies θB < 0$implies \theta_{\mathrm{B}} > 90^\circ implies \cos\theta_{\mathrm{B}} < 0$ (negative).

This makes the ratio K = positivenegative < 0$K = \frac{\text{positive}}{\text{negative}} < 0$ (negative), which accurately validates the statement.

Pattern Recognition

Meniscus geometry directly correlates with the sign of θ$\cos\theta$: acute contact angle = concave (wetting fluid), obtuse contact angle = convex (non-wetting fluid).

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Related Formula

h = (2T θ)/(ρ g r)$$h = \frac{2T\cos\theta}{\rho g r}$$ [cite: 694]

Core Logic

First, calculate the vertical height h$h$ using CGS units: [cite: 694]

• T = 70 dyn/cm$T = 70\ \text{dyn/cm}$ [cite: 83]
• θ = 0° = 1$\cos\theta = \cos 0^{\circ} = 1$ [cite: 83]
• ρ = 1 g/cm³$\rho = 1\ \text{g/cm}^3$ [cite: 694]
• g = 980 cm/s²$g = 980\ \text{cm/s}^2$ [cite: 694]
• r = 0.1 mm = 10⁻² cm$r = 0.1\ \text{mm} = 10^{-2}\ \text{cm}$ [cite: 83, 694]

h = 2 × 70 × 11 × 980 × 10⁻² = (140)/(9.8) = (100)/(7) cm$$h = \frac{2 \times 70 \times 1}{1 \times 980 \times 10^{-2}} = \frac{140}{9.8} = \frac{100}{7}\ \text{cm}$$ [cite: 694]

Since the tube is inclined at 30°$30^{\circ}$ to the vertical, the angle it makes with the horizontal is 60°$60^{\circ}$[cite: 83, 694]. The relationship between vertical height h$h$ and slant length l$l$ is: [cite: 694]

60° = (h)/(l) l = h 60° = 2h√(3)$$\sin 60^{\circ} = \frac{h}{l} \implies l = \frac{h}{\sin 60^{\circ}} = \frac{2h}{\sqrt{3}}$$ [cite: 694]

l = (100)/(7) × 2√(3) = 2007√(3) ≈ 16.49 cm$$l = \frac{100}{7} \times \frac{2}{\sqrt{3}} = \frac{200}{7\sqrt{3}} \approx 16.49\ \text{cm}$$ [cite: 696, 697, 698]

Checking option values, (82)/(5) = 16.4 cm$\frac{82}{5} = 16.4\ \text{cm}$, which is closest[cite: 85, 698].

Pattern Recognition

When a capillary tube is tilted, the vertical height of the fluid column remains constant to maintain hydrostatic pressure balance[cite: 694]. Thus, the length of the liquid along the slant always scales as l = (h)/( α)$l = \frac{h}{\cos\alpha}$ where α$\alpha$ is the tilt angle relative to the vertical line[cite: 83, 694].

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids

Related Formula

The work done W$W$ in expanding surface area with surface tension S$S$ is given by:

Core Logic

By volume conservation during splitting :

Total change in area gives work expression:

Step 1: Set up Proportions

For n = 27$n = 27$ drops:

For n = 64$n = 64$ drops:

Pattern Recognition

Work scales scaling-wise linearly with the key multiplier index (n1/3 - 1)$(n^{1/3} - 1)$. Taking ratios between targets directly avoids calculations of constants.

Chapter Mix

Class 11 Physics: Mechanical Properties of Fluids