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Q. No.A submarine having a fixed volume is floating submerged underwater. Air, at high pressure, is pumped into the submarine using pipes. Due to this, the submarine will:
1.
rise.
2.
sink.
3.
float in the same position.
4.
either rise or sink depending on the air pressure.
Subtopic: Pressure |
Level 3: 35%-60%
Hints
Which of the following diagrams correctly illustrates the streamline flow of a liquid out of a tank?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Types of Flows |
63%
Level 2: 60%+
Hints
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A viscous liquid flows slowly through a pipe of cross-sectional radius \(R.\) The speed of the particles is a function of the distance from the axis of the pipe.
Assume that the flow is smooth. The variation of \(v\) vs \(r\) is best given by the graph:
Assume that the flow is smooth. The variation of \(v\) vs \(r\) is best given by the graph:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Viscosity |
53%
Level 3: 35%-60%
Hints
The arrangement shows two pistons \(P_1,P_2\) with a rigid connecting rod \(C\) so that they can slide together with respect to the two fixed cylinders of cross-sectional areas \(A_1,A_2\) respectively. The two cylinders are connected by means of two pipes to a small cylinder (of area \(A\)) with a piston at the bottom on which is applied a force \(F.\) The interior of the pipes and cylinder is filled with an incompressible oil. Ignore any pressure variations due to gravity. The net force on the two pistons \(P_1, P_2\) is:
1. \(\dfrac{F}{A}(A_1+A_2)\) to right.
2. \(\dfrac{F}{A}(A_1+A_2)\) to left.
3. \(\dfrac{F}{A}(A_2-A_1)\) to right.
4. \(\dfrac{F}{A}(A_2-A_1)\) to left.
1. \(\dfrac{F}{A}(A_1+A_2)\) to right.
2. \(\dfrac{F}{A}(A_1+A_2)\) to left.
3. \(\dfrac{F}{A}(A_2-A_1)\) to right.
4. \(\dfrac{F}{A}(A_2-A_1)\) to left.
Subtopic: Pressure |
52%
Level 3: 35%-60%
Hints
A thin spherical shell of radius \(R,\) thickness \(t,\) made of a metal of density \(\large{\rho}_{\small{S}},\) floats half submerged in a vessel containing a liquid of density \(\large{\rho}_{\small{L}}.\) The ratio \(\dfrac{\large{\rho}_{\small{S}}}{\large{\rho}_{\small{L}}}\) is equal to:
| 1. | \(\dfrac{R}{6t}\) | 2. | \(\dfrac{R}{3t}\) |
| 3. | \(\dfrac{6t}{R}\) | 4. | \(\dfrac{3t}{R}\) |
Subtopic: Archimedes' Principle |
Level 3: 35%-60%
Hints
A large vessel of liquid of density \(\rho\) is contained in a tank. The tank is pulled towards the right with a constant acceleration \(a.\) The upper level of the liquid is not shown in the diagram. Then, the pressures at \(A\) and \(B\) are related by:
1. \(P_A=P_B\)
2. \(P_A-P_B=L\rho a\)
3. \(P_B-P_A=L\rho a\)
4. \(P_A-P_B=L\rho \sqrt{a^2+g^2}\)
1. \(P_A=P_B\)
2. \(P_A-P_B=L\rho a\)
3. \(P_B-P_A=L\rho a\)
4. \(P_A-P_B=L\rho \sqrt{a^2+g^2}\)
Subtopic: Pressure |
56%
Level 3: 35%-60%
Hints
A liquid of density \(\rho\) flows through a bent tube of cross-section \(A,\) with a speed \(v.\) The liquid enters at point \(A\) and exits at \(B\) in the opposite direction. The radius of the bend is \(R.\) The tube lies on a horizontal table. The force required to hold the tube equals:
1. \(\rho Av^2\)
2. \(2\rho Av^2\)
3. \(\sqrt2\rho Av^2\)
4. \(\rho v^2\pi R^2\)
1. \(\rho Av^2\)
2. \(2\rho Av^2\)
3. \(\sqrt2\rho Av^2\)
4. \(\rho v^2\pi R^2\)
Subtopic: Pressure |
58%
Level 3: 35%-60%
Hints
The bob (mass : \(m\)) of a simple pendulum is suspended from a long wire of length \(L.\) When this bob is submerged in a fluid of density \(\rho,\) it is observed by means of a careful measurement that the extension in the wire is halved. The volume of the bob is:
| 1. | \(\dfrac{m}{\rho}\) | 2. | \(\dfrac{2m}{\rho}\) |
| 3. | \(\dfrac{m}{2\rho}\) | 4. | \(\dfrac{3m}{2\rho}\) |
Subtopic: Archimedes' Principle |
61%
Level 2: 60%+
Hints
A tank of uniform cross-section is filled with water. The pressure at the bottom of the tank is \( P_0,\) and the volume of water is \(V_0.\) Ignore atmospheric pressure. The potential energy of the water in the tank (taking the base as the reference) is:
| 1. | \( P_0V_0\) | 2. | \(2 P_0V_0\) |
| 3. | \({\Large\frac{ P_0V_0}2}\) | 4. | \({\Large\frac{ P_0V_0}4}\) |
Subtopic: Pressure |
55%
Level 3: 35%-60%
Hints
Water is under high pressure within a tank. When a hole is made at the top of the tank, a stream of water rises up vertically to a height \(H\) above the hole. Assume the flow to be streamlined. The water pressure (gauge pressure) at the top of the tank, initially, was: (\(\rho\) density of water)
| 1. | \(H\rho g\) | 2. | \(\dfrac{H\rho g}{2}\) |
| 3. | \(2 H\rho g\) | 4. | \(\sqrt 2 H \rho g\) |
Subtopic: Bernoulli's Theorem |
64%
Level 2: 60%+
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