In the experiment for measurement of viscosity η$\eta$ of given liquid with a ball having radius R$R$ , consider following statements. A. Graph between terminal velocity V and R will be a parabola B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of η$\eta$ will change. Choose the correct answer from the options given below:

Core Logic

Let's audit each fluid mechanics assertion:

Statement A: Incorrect. Surface tension arises because surface molecules possess higher potential energy compared to interior bulk molecules due to net cohesive forces pulling inward.

Statement B: Incorrect. With rising temperatures, cohesive forces in liquids weaken, causing viscosity to decrease.

Statement C: Correct. In gases, viscosity is governed by molecular collisions. Higher temperature leads to increased thermal activity and momentum exchange, increasing viscosity.

Statement D: Correct. Critical velocity and turbulence parameters are completely defined by the dimensionless Reynolds number.

Statement E: Correct. If streamlines intersected, a fluid particle at that spatial node would have two distinct velocity directions, violating steady-state constraints.

Step 1: Final Conclusion

Statements C, D, and E are correct, leading to option (2).

Pattern Recognition

Contrast Liquid vs Gas viscosity trends under temperature increments: Liquids down (intermolecular bounds weaken), Gases up (random thermal diffusion and collision rates escalate).

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