Mechanical Properties of Fluids - live session

1.

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 $ω$ . The force exerted by liquid at the other end is
1.   $\frac{{Mω}^{2} L}{2}$
2.   ${MLω}^{2}$
3.   $\frac{{Mω}^{2} L}{4}$
4.   $\frac{M L^{2} ω^{2}}{2}$

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.	$\dfrac{vR^2}{n^2r^2}$	2.	$\dfrac{vR^2}{nr^2}$
3.	$\dfrac{vR^2}{n^3r^2}$	4.	$\dfrac{v^2R}{nr}$

3.

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

4.

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

5.

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) $10^{5} N / m$
(2) $2 \times 10^{5} N / m$
(3) Zero
(4) Infinity

6.

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

7.

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

8.

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

9.

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

10.

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) $5 \times (4)^{\frac{1}{3}}$ cm per sec (d) $5 \times \sqrt{2}$ cm per sec

11.

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 ${kgm}^{- 3}$ . The velocity with which gasoline begins to shoot out of the hole is
(a) 27.8 ${ms}^{- 1}$ (b) 41.0 ${ms}^{- 1}$
(c) 9.6 ${ms}^{- 1}$ (d) 19.7 ${ms}^{- 1}$

12.

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) $\sqrt{\frac{2 h}{g}}$
(2) $\sqrt{\frac{2 h}{g} \cdot \frac{D}{d}}$
(3) $\sqrt{\frac{2 h}{g} \cdot \frac{d}{D}}$
(4) $\sqrt{\frac{2 h}{g}} (\frac{d}{D - d})$

13.

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

14.

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

15.

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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1.	\(\dfrac{vR^2}{n^2r^2}\)	2.	\(\dfrac{vR^2}{nr^2}\)
3.	\(\dfrac{vR^2}{n^3r^2}\)	4.	\(\dfrac{v^2R}{nr}\)

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

1.	\(l\) decreases and \(h\) increases
2.	\(l\) increases and \(h\) decreases
3.	Both \(l\) and \(h\) increase
4.	Both \(l\) and \(h\) decrease

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