A solid steel ball of diameter 3.6~mm$3.6\mathrm{~mm}$ acquired terminal velocity 2.45×10⁻²~m/s$2.45\times10^{-2}\mathrm{~m/s}$ while falling under gravity through an oil of density 925~kg~m⁻³$925\mathrm{~kg~m}^{-3}$. Take density of steel as 7825~kg~m⁻³$7825\mathrm{~kg~m}^{-3}$ and g as 9.8~m/s²$9.8\mathrm{~m/s}^{2}$. The viscosity of the oil in SI unit is :
A.2.18
B.2.38
C.1.68
D.1.99
Solution & Explanation
Related Formula
Terminal velocity vₜ$v_t$ of a spherical body falling through a viscous fluid is given by Stokes' Law:
vₜ = (2)/(9) r² g (ρbody - ρfluid)η$$v_t = \frac{2}{9} \frac{r^2 g (\rho_{\text{body}} - \rho_{\text{fluid}})}{\eta}$$
Hence, the viscosity coefficient η$\eta$ is:
η = (2)/(9) r² g (ρbody - ρfluid)vₜ$$\eta = \frac{2}{9} \frac{r^2 g (\rho_{\text{body}} - \rho_{\text{fluid}})}{v_t}$$
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$6\text{ cm}^{2}$ and 3 cm²$3\text{ cm}^{2}$ respectively. The rate of flow will be ____ cm³$\text{cm}^{3}$/s. (take g = 10 m/s²$\text{m/s}^{2}$)
The figure illustrates a Venturi meter setup with water flowing through a variable cross-section tube.
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)$\rho g h = \frac{1}{2}\rho (V_2^2 - V_1^2)$ 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
Q38jee_main_2026_21_jan_eveningSurface Tension
Surface tension of two liquids (having same densities), T₁$T_{1}$ and T₂$T_{2}$, are measured using capillary rise method utilizing two tubes with inner radii of r₁$r_{1}$ and r₂$r_{2}$ where r₁ > r₂$r_{1} > r_{2}$. The measured liquid heights in these tubes are h₁$h_{1}$ and h₂$h_{2}$ respectively. [Ignore the weight of the liquid about the lowest point of miniscus]. The heights h₁$h_{1}$ and h₂$h_{2}$ and surface tensions T₁$T_{1}$ and T₂$T_{2}$ 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)$$h = \frac{2T\cos\theta}{\rho g r}$$
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 ∝ (1)/(r)$$h \propto \frac{1}{r}$$
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 ∝ 1/r$h \propto 1/r$ is a foundational inverse relationship in capillary action.
Chapter Mix
Class 11 Physics: Mechanical Properties of Fluids
Q47jee_main_2026_21_jan_eveningTerminal Velocity
The terminal velocity of a metallic ball of radius 6 mm$6 \text{ mm}$ in a viscous fluid is 20 cm/s$20 \text{ cm/s}$. The terminal velocity of another ball of same material and having radius 3 mm$3 \text{ mm}$ in the same fluid will be ________ cm/s.
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 ∝ r²$v_T \propto r^2$.
Terminal velocity is directly proportional to the square of the radius. Halving the radius (6 → 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
Q33jee_main_2026_22_january_morningPascal'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$\text{Statement I is true but Statement II is false}$
B.Both Statement I and Statement II are false$\text{Both Statement I and Statement II are false}$
C.Both Statement I and Statement II are true$\text{Both Statement I and Statement II are true}$
D.Statement I is false but Statement II is true$\text{Statement I is false but Statement II is true}$
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
Q34jee_main_2026_22_january_eveningCapillarity 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 ____%.
Practice past-year questions one chapter at a time. Pick an exam → subject → chapter and get every PYQ for that topic — pulled together from all past papers — with the chapter's key formulas alongside.
