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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. vR²/n²r²
2. vR²/nr²
3. vR²/n³r²
4. v²R/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:\(\text { Energy }=4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \text { is released } \)

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 $70 {\mathrm{cm}}^3/\sec$. 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) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}·\frac{D}{d}}$
(3) $\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}·\frac{d}{D}}$                   
(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:
                      

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