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Q. No.Consider a water tank shown in the figure. It has one wall at \(x=L\) and can be taken to be very wide in the \(z\) direction. When filled with a liquid of surface tension \(S\) and density \(\rho,\) the liquid, surface makes angle \(\theta_{0}\left(\theta_0 \ll 1\right)\) with the \(x\text-\)axis at \(x=L.\) If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is:
(take \(\theta(x)=\sin \theta(x)=\tan \theta(x)=\dfrac{d y}{d x}, g\) is the acceleration due to gravity)
(take \(\theta(x)=\sin \theta(x)=\tan \theta(x)=\dfrac{d y}{d x}, g\) is the acceleration due to gravity)
| 1. | \(\dfrac{d^2 y}{d x^2}=\sqrt{\dfrac{\rho g}{S}}\) | 2. | \(\dfrac{d y}{d x}=\sqrt{\dfrac{\rho g}{S}} x\) |
| 3. | \(\dfrac{d^2 y}{d x^2}=\dfrac{\rho g}{S} x\) | 4. | \(\dfrac{d^2 y}{d x^2}=\dfrac{\rho g}{S} y\) |
Subtopic: Surface Tension |
From NCERT
NEET - 2025
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A thin flat circular disc of radius \(4.5~\text {cm}\) is placed gently over the surface of water. If the surface tension of water is \(0.07~\text{Nm}^{-1},\) then the excess force required to take it away from the surface is:
1. \(198~\text{N}\)
2. \(1.98~\text{mN}\)
3. \(99~\text{N}\)
4. \(19.8~\text{mN}\)
1. \(198~\text{N}\)
2. \(1.98~\text{mN}\)
3. \(99~\text{N}\)
4. \(19.8~\text{mN}\)
Subtopic: Surface Tension |
52%
From NCERT
NEET - 2024
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A wire of length \(L\) and radius \(r(r\ll L)\) is kept floating on the surface of a liquid of density \(\rho.\) The maximum radius of the wire for which it may not sink is:
(the surface tension of liquid is \(T\))
(the surface tension of liquid is \(T\))
| 1. | \(\sqrt { \dfrac{T}{\rho g}}\) | 2. | \(\sqrt { \dfrac{2T}{\rho g}}\) |
| 3. | \(\sqrt{\dfrac{2T\rho}{\pi g}}\) | 4. | \(\sqrt{\dfrac{2T} {\pi \rho g}}\) |
Subtopic: Surface Tension |
61%
From NCERT
NEET - 2024
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The pressure experienced by a swimmer \(20~\text{m}\) below the water surface in a lake is appropriately:
(Given density of water = \(10^3 ~\text{kgm}^{-3},~ g=10 ~\text{ms}^{-2} \) and \(1~\text{atm} = 10^5~\text{Pa}\))
(Given density of water = \(10^3 ~\text{kgm}^{-3},~ g=10 ~\text{ms}^{-2} \) and \(1~\text{atm} = 10^5~\text{Pa}\))
| 1. | \(1~\text{atm}\) | 2. | \(2~\text{atm}\) |
| 3. | \(3~\text{atm}\) | 4. | \(4~\text{atm}\) |
Subtopic: Pressure |
69%
From NCERT
NEET - 2024
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An ideal fluid is flowing in a non-uniform cross-sectional tube \(XY\) (as shown in the figure) from end \(X\) to end \(Y.\) If \(K_1\) and \(K_2\) are the kinetic energies per unit volume of the fluid at \(X\) and \(Y\) respectively, the correct relationship between \(K_1\) and \(K_2\) is:
| 1. | \(K_1=K_2\) | 2. | \({2K}_1={K}_2\) |
| 3. | \({K}_1>{K}_2\) | 4. | \({K}_1<{K}_2\) |
Subtopic: Bernoulli's Theorem |
69%
From NCERT
NEET - 2024
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The venturi-meter works on:
| 1. | The principle of perpendicular axes |
| 2. | Huygen's principle |
| 3. | Bernoulli's principle |
| 4. | The principle of parallel axes |
Subtopic: Bernoulli's Theorem |
85%
From NCERT
NEET - 2023
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The amount of energy required to form a soap bubble of radius \(2~\text{cm}\) from a soap solution is nearly:
\((\)the surface tension of soap solution \(0.03~\text{Nm}^{-1})\)
1. \(50.1 \times 10^{-4}~\text{J}\)
2. \(30.16 \times 10^{-4}~ \text{J}\)
3. \(5.06 \times 10^{-4} ~\text{J}\)
4. \(3.01\times 10^{-4} ~\text{J}\)
\((\)the surface tension of soap solution \(0.03~\text{Nm}^{-1})\)
1. \(50.1 \times 10^{-4}~\text{J}\)
2. \(30.16 \times 10^{-4}~ \text{J}\)
3. \(5.06 \times 10^{-4} ~\text{J}\)
4. \(3.01\times 10^{-4} ~\text{J}\)
Subtopic: Surface Tension |
62%
From NCERT
NEET - 2023
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Which of the following statements is not true?
| 1. | The coefficient of viscosity is a scalar quantity. |
| 2. | Surface tension is a scalar quantity. |
| 3. | Pressure is a vector quantity. |
| 4. | Relative density is a scalar quantity. |
Subtopic: Pressure |
72%
From NCERT
NEET - 2023
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The viscous drag acting on a metal sphere of diameter \(1\) mm, falling through a fluid of viscosity \(0.8\) Pa-s with a velocity of \(2\) m s–1 is nearly equal to:
| 1. | \(15\times 10^{-3}~\text{N}\) | 2. | \(30\times 10^{-3}~\text{N}\) |
| 3. | \(1.5\times 10^{-3}~\text{N}\) | 4. | \(20\times 10^{-3}~\text{N}\) |
Subtopic: Stokes' Law |
63%
From NCERT
NEET - 2023
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If a soap bubble expands, the pressure inside the bubble:
1. is equal to the atmospheric pressure
2. decreases
3. increases
4. remains the same
1. is equal to the atmospheric pressure
2. decreases
3. increases
4. remains the same
Subtopic: Surface Tension |
70%
From NCERT
NEET - 2022
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