Mechanical Properties of Fluids - live session - 29th NovContact Number: 9667591930 / 8527521718

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A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega $. The force exerted by liquid at the other end is

1. $\frac{{\mathrm{M\omega}}^{2}\mathrm{L}}{2}$

2. ${\mathrm{ML\omega}}^{2}$

3. $\frac{{\mathrm{M\omega}}^{2}\mathrm{L}}{4}$

4. $\frac{M{L}^{2}{\omega}^{2}}{2}$

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, then the speed of ejection of the liquid through the holes will be:

1. vR^{2}/n^{2}r^{2}

2. vR^{2}/nr^{2}

3. vR^{2}/n^{3}r^{2}

4. v^{2}R/nr

Water rises to a height h in capillary tube . If the length of capillary tube above the surface of water is made less than h, then

(1) water rises upto the tip of capillary tube and then starts overflowing like a fountain

(2) water rises upto the top of capillary tube and stays there without overflowing

(3) water rises upto a point a little below the top and stays there

(4) water does not rise at all

A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then:\(\text { Energy }=4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \text { is released } \)

1. | Energy = \(4 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 2. | Energy =\(3 V T\left(\frac{1}{r}+\frac{1}{R}\right)\) is released |

3. | Energy =\(3 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 4. | Energy is neither released nor absorbed |

A siphon in use is demonstrated in the following figure. The density of the liquid flowing in siphon is 1.5 gm/cc. The pressure difference between the point P and S will be

(1) ${10}^{5}\mathrm{N}/\mathrm{m}$

(2) $2\times {10}^{5}\mathrm{N}/\mathrm{m}$

(3) Zero

(4) Infinity

A barometer tube reads 76 cm of mercury. If the tube is gradually inclined at an angle of 60^{o} with vertical, keeping the open end immersed in the mercury reservoir, the length of the mercury column will be

(a) 152 cm (b) 76 cm

(c) 38 cm (d) $38\sqrt{3}$ cm

A hemispherical bowl just floats without sinking in a liquid of density $1.2\times {10}^{3}$ $\mathrm{kg}/{\mathrm{m}}^{3}$. If the outer diameter and the density of the material of the bowl are 1 m and $2\times {10}^{4}$ $\mathrm{kg}/{\mathrm{m}}^{3}$ respectively, then the inner diameter of the bowl will be:

1. 0.94 m

2. 0.97 m

3. 0.98 m

4. 0.99 m

In which one of the following cases will the liquid flow in a pipe be most streamlined ?

(1) Liquid of high viscosity and high density flowing through a pipe of small radius

(2) Liquid of high viscosity and low density flowing through a pipe of small radius

(3) Liquid of low viscosity and low density flowing through a pipe of large radius

(4) Liquid of low viscosity and high density flowing through a pipe of large radius

A cylindrical tank has a hole of $1{\mathrm{cm}}^{2}$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70{\mathrm{cm}}^{3}/\mathrm{sec}$. then the maximum height up to which water can rise in the tank is

(1) 2.5 cm

(2) 5 cm

(3) 10 cm

(4) 0.25 cm

Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be

(a) 10 cm per sec (b) 2.5 cm per sec

(c) $5\times (4{)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ cm per sec (d) $5\times \sqrt{2}$ cm per sec

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 ${\mathrm{kgm}}^{-3}$. The velocity with which gasoline begins to shoot out of the hole is

(a) 27.8 ${\mathrm{ms}}^{-1}$ (b) 41.0 ${\mathrm{ms}}^{-1}$

(c) 9.6 ${\mathrm{ms}}^{-1}$ (d) 19.7 ${\mathrm{ms}}^{-1}$

A streamlined body falls through air from a height h on the surface of a liquid. If d and D(D > d) represents the densities of the material of the body and liquid respectively, then the time after which the body will be instantaneously at rest, is

(1) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}$

(2) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}\xb7\frac{D}{d}}$

(3) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}\xb7\frac{d}{D}}$

(4) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}}\left(\frac{d}{D-d}\right)$

A wooden block with a coin placed on its top, floats in water as shown in fig. The distance l and h are shown there. After some time the coin falls into the water. Then:

1. | l decreases and h increases |

2. | l increases and h decreases |

3. | Both l and h increase |

4. | Both l and h decrease |

The pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. The ratio between their volumes is

(1) 102 : 101

(2) $(102{)}^{3}:(101{)}^{3}$

(3) 8 : 1

(4) 2 : 1

By inserting a capillary tube up to a depth l in water, the water rises to a height of h ( h<l). If the lower end of the capillary is closed inside the water and the capillary is taken out and closed-end opened, to what height the water will remain in the tube?

(1) Zero

(2) l+h

(3) 2h

(4) h

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