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Q. No.The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74~\text{m}^3\) water per minute through a circular opening of \(2~\text{cm}\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:
1. \(6.0~\text{m}\)
2. \(4.8~\text{m}\)
3. \(9.6~\text{m}\)
4. \(2.9~\text{m}\)
1. \(6.0~\text{m}\)
2. \(4.8~\text{m}\)
3. \(9.6~\text{m}\)
4. \(2.9~\text{m}\)
Subtopic: Properties of Fluids |
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Level 2: 60%+
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Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d\). The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_1\) and in the other, \(x_2\). when both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is:
1. \( \frac{3}{4} g d S\left(x_2-x_1\right)^2 \)
2. \( \frac{1}{4} g d S\left(x_2-x_1\right)^2 \)
3. \(g d S\left(x_2^2-x_1^2\right) \)
4. \( g d S\left(x_2-x_1\right)^2\)
Subtopic: Properties of Fluids |
56%
Level 3: 35%-60%
JEE
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If \(\rho\) is the density and \(\eta\) is the coefficient of viscosity of fluid which flows with a speed \(v\) in the pipe of diameter \(d,\) the correct formula for the Reynolds number \(R_e\) is:
1. \( \mathrm{R}_e=\frac{\eta \mathrm{d}}{\rho \mathrm{v}} \)
2. \(\mathrm{R}_{\mathrm{e}}=\frac{\rho \mathrm{v}}{\eta \mathrm{d}} \)
3. \( \mathrm{R}_e=\frac{\rho v d}{\eta} \)
4. \(R_e=\frac{\eta}{\rho v d}\)
1. \( \mathrm{R}_e=\frac{\eta \mathrm{d}}{\rho \mathrm{v}} \)
2. \(\mathrm{R}_{\mathrm{e}}=\frac{\rho \mathrm{v}}{\eta \mathrm{d}} \)
3. \( \mathrm{R}_e=\frac{\rho v d}{\eta} \)
4. \(R_e=\frac{\eta}{\rho v d}\)
Subtopic: Properties of Fluids |
85%
Level 1: 80%+
JEE
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Given below are two statements:
| Assertion (A): | When toothpaste is pressed (squeezed), it follows Pascal’s law. |
| Reason (R): | When pressure is applied to a fluid, it is transmitted equally throughout the fluid in all directions and on the walls of the container. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Properties of Fluids |
82%
Level 1: 80%+
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A long cylindrical vessel is half-filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of the vessel is \(5 ~\text{cm}\) and its rotational speed is \(2\) rotations per second, then the difference in the heights between the centre and the sides \(\text{(in cm),}\) will be
1. \(2.0\)
2. \(0.1\)
3. \(0.4\)
4. \(1.2\)
1. \(2.0\)
2. \(0.1\)
3. \(0.4\)
4. \(1.2\)
Subtopic: Properties of Fluids |
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Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \(0.01 ~\text{cm}^3\) of oleic acid per \(\text{cm}^3\) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \(4~\text{cm}^2\) by considering \(100\) spherical drops of radius \(\left(\dfrac{3}{40 \pi}\right)^{\dfrac{1}{3}} \times 10^{-3}~ \text{cm} \). Then the thickness of oleic acid will be:
1. \(12\times10^{-14}~\text{m}\)
2. \(25\times10^{-14}~\text{m}\)
3. \(36\times10^{-14}~\text{m}\)
4. \(48\times10^{-14}~\text{m}\)
1. \(12\times10^{-14}~\text{m}\)
2. \(25\times10^{-14}~\text{m}\)
3. \(36\times10^{-14}~\text{m}\)
4. \(48\times10^{-14}~\text{m}\)
Subtopic: Properties of Fluids |
72%
Level 2: 60%+
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Consider following statements:
Choose the correct answer from the options given below:
1. (A), (D), (E) only
2. (A), (B), (C) only
3. (C), (D), (E) only
4. (B), (C), (D) only
| (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:
1. (A), (D), (E) only
2. (A), (B), (C) only
3. (C), (D), (E) only
4. (B), (C), (D) only
Subtopic: Properties of Fluids |
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