The loss in weight of a lead block is \(3\) times in liquid \(A\) compared to that in liquid \(B\). In both cases, the block is half immersed. If \(\rho_A, \rho_B\) be the densities of the liquids and \(\rho_L\) the density of lead, then:

1. \(3\rho_A=\rho_B\)
2. \(\dfrac32\rho_A=\rho_B\)
3. \(\rho_A=\dfrac32\rho_B\)
4. \(\rho_A=3\rho_B\)
Subtopic:  Archimedes' Principle |
 58%
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A block of wood is immersed in water (assume that the wood is impervious to water), and it floats half immersed. It is placed in an elevator which is accelerating upward. Then,

1. the block floats, slightly more of it out of the water.
2. the block floats, slightly less of it out of the water.
3. the block floats, half-immersed.
4. the block sinks completely.
Subtopic:  Archimedes' Principle |
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Given below are two statements: 

Assertion (A): Water flows through a smooth horizontal tube with a narrowing cross-section and its pressure increases.
Reason (R): Bernoulli's equation for fluids states that \(P+\dfrac{1}{2}\rho v^2+\rho gh= \) constant along a streamline.
 
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. (A) is False but (R) is True.
Subtopic:  Bernoulli's Theorem |
 61%
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A small tube containing air at atmospheric pressure (\(P=76\) cm of Hg) has a mercury column of the length of \(19\) cm. The tube is initially horizontal, then it is turned so that the open end is upward and the tube is vertical.
                            
The length of the trapped air column:

1. increases by \(10\) cm.
2. decrease by \(10\) cm.
3. increases by \(8\) cm.
4. decreases by \(8\) cm.
Subtopic:  Pressure |
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A block of ice floats in water, in a beaker at \(0\)°C, nearly. The ice melts slowly until the beaker is full of water. As a result, the pressure at the bottom:
1. increases slowly.
2. decreases slowly.
3. first increases and then decreases.
4. remains constant.
Subtopic:  Pressure |
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A liquid of density \(\rho\) is forced out through a small hole by means of a piston of cross-section 'A', on which a force \(F\) is applied. The flow is streamline. The liquid stream strikes the ground at a distance '\(x\)' in front of the hole. The hole is in the middle of the right face and its height is '\(h\)' above the ground. The expression for \(x^2\) is:
                     
1. \(\dfrac{4 F h}{A \rho g}\) 2. \(\dfrac{2 F h}{A \rho g}\)
3. \(\dfrac{F h}{A \rho g}\) 4. \(\dfrac{F h}{2 A \rho g}\)
Subtopic:  Bernoulli's Theorem |
 52%
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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 |
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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%
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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:
1. 2.
3. 4.
Subtopic:  Viscosity |
 51%
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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.
Subtopic:  Pressure |
 53%
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