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Q. No.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:
1.
2.
3.
4.
Subtopic: Viscosity |
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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 |
53%
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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 |
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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 |
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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 |
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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 bob is:
| 1. | \(\dfrac{m}{\rho}\) | 2. | \(\dfrac{2m}{\rho}\) |
| 3. | \(\dfrac{m}{2\rho}\) | 4. | \(\dfrac{3m}{2\rho}\) |
Subtopic: Archimedes' Principle |
62%
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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 |
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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 |
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A pair of soap bubbles cling together to form a double-bubble as shown: their respective radii are \(3R,R.\) The radius of their interface \((PQ)\) is:
| 1. | \(2R\) | 2. | \(5R\) |
| 3. | \(\dfrac{3R}{4}\) | 4. | \(\dfrac{3R}{2}\) |
Subtopic: Surface Tension |
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The surface tension of soapy water is \(S.\) When bubbles are blown with soapy water, one bubble of radius \(r\) is formed within another of radius \(3r.\) The excess pressure within the smaller bubble, relative to the atmospheric pressure is:
| 1. | \(\dfrac{4S}{r}\) | 2. | \(\dfrac{8S}{3r}\) |
| 3. | \(\dfrac{8S}{r}\) | 4. | \(\dfrac{16S}{3r}\) |
Subtopic: Surface Tension |
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