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. $\rho v^2\pi R^2$

Subtopic: Pressure |

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Q14:

The bob (mass :

m

$m$ ) of a simple pendulum is suspended from a long wire of length

L .

$L.$ When this bob is submerged in a fluid of density

ρ,

$\rho,$ 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 |

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Q15:

A tank of uniform cross-section is filled with water. The pressure at the bottom of the tank is

P_{0},

$P_0,$ and the volume of water is

V_{0} .

$V_0.$ 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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Q16:

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

$H$ above the hole. Assume the flow to be streamlined. The water pressure (gauge pressure) at the top of the tank, initially, was: (

ρ

$\rho$ 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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Q17:

A pair of soap bubbles cling together to form a double-bubble as shown: their respective radii are

3 R, R .

$3R,R.$ The radius of their interface

(P Q)

$(PQ)$ is:

1.	$2R$	2.	$5R$
3.	$\dfrac{3R}{4}$	4.	$\dfrac{3R}{2}$

Subtopic: Surface Tension |

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Q18:

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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Q19:

Consider a tank full of water with an outlet at the bottom. As the outlet valve is opened, and water flows out, the pressure inside the tank near the outlet:

1.	increases.
2.	decreases.
3.	remains unchanged.
4.	increases and then quickly returns to normal.

Subtopic: Pressure |

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Q20:

Water flows from a small hole at the bottom of a rectangular tank at

$10$ m/s after it had been filled for

$20$ min. For how much time should the empty tank be filled at the same rate so that the speed of efflux is doubled? (i.e. it becomes

$20$ m/s)
1.

$40$ min
2.

$80$ min
3.

$160$ min
4.

$320$ min

Subtopic: Bernoulli's Theorem |

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Q21:

A viscous liquid is flowing through a straight tube under the action of a pressure difference across the ends of the tube. The tube is aligned with the

$x$ -axis. The force exerted on the tube by the liquid has the form:

$(a,b>0)$

1.	$a\hat i$	2.	$-a\hat i$
3.	$a\hat i+b\hat j$	4.	$-a\hat i+b\hat j$

Subtopic: Viscosity |

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Q12:

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.

$P_A-P_B=L\rho \sqrt{a^2+g^2}$

Subtopic: Pressure |

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