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A non-viscous liquid of constant density${10}^3 kg/m^3$flows in streamline motion along a
vertical tube PQ of variable cross-section. Height of P and Q are 2 m and 2.5 m
respectively . Area of tube at Q=3 time area of tube at P. Find the work done per unit
volume by pressure as liquid flows from P to Q. Speed of liquid at P is 3 m/s (g= 10
m/s${}^2$).
(1) 2000 j/m${}^3$
(2) 1000 j/m${}^3$  
(3) 1575 j/m${}^3$ 
(4) 9000 j/m${}^3$

Two equal drops of water each of radius r are falling through air with a steady velocity
of 8 cm/s . The two drops combine to form a big drop. The terminal velocity of big
drop will be 
(1) $8{\left(2\right)}^{\frac{2}{3}} cm/s$
(2) $16{\left(2\right)}^{\frac{2}{3}} m$
(3) $4{\left(2\right)}^{\frac{2}{3}} cm/s$
(4) 32 cm/s

An open vessel containing water is given a constant acceleration a in the horizontal
direction direction. Then the free surface of water gets sloped with the horizontal at an
angle $\theta$  given by 
(1) $\theta ={\tan }^{-1 }\left(\frac{a}{g}\right)$
(2) $\theta ={\tan }^{-1 }\left(\frac{g}{a}\right)$
(3) $\theta =si{n}^{-1 }\left(\frac{a}{g}\right)$
(4) $\theta ={\cos }^{-1 }\left(\frac{g}{a}\right)$

Water enters a house through a pipe 2 cm inside diameter at an absolute pressure 4
$\times {10}^5$ Pa (about 4 atmospheres). The pipe leading to second floor bathroom 5 m
above is 1 cm in diameter. The flow velocity at the inlet pipe is 4 m/s . The pressure in
the bathroom.
(1) 2 $\times {10}^5$ pa 
(2) 2.3 $\times {10}^5$ Pa
(3) 3 $\times {10}^5$ Pa
(4) 3.3 $\times {10}^5$ Pa

There is a smaller hole in a hollow sphere. The water eners in it when it is taken to a
depth of 40 cm under water. The surface tension of water is 0.07 N/m. The diameter of
hole is 
(1) 7 mm 
(2) 0.07 mm 
(3) 0.0007 mm  
(4) 0.7 m 
 

A unifromly tapering vessel of height h whose lower and upper radii and r and R is
completely filled with a liquid of density p. The force thatt acts on the base of the
vessel due to the liquid is 
(1) ${\mathrm{\pi R}}^2\mathrm{hpg}$
(2)  ${\mathrm{\pi }}^2\mathrm{hpg}$
(3) $\mathrm{\pi }{\left(\frac{\mathrm{R}+\mathrm{r}}{2}\right)}^2$hpg 
(4) $\frac{1}{3}\mathrm{\pi }({\mathrm{R}}^2-{\mathrm{r}}^2)\mathrm{hpg}$

If two soap bubbles of different radii are in communication with each other 
(1) air flow larger bubblue inot the smaller one until the two bubbles are of equal size. 
(2) the size of the bubble reamains the same 
(3) air flows from the smaller bubble into the larger one and larger bubble grows       
     at the expense of the smaller one 
(4) the air flows from the larger bubble into the smaller bubble until the radius of the   
     smaller one becomes equal to that of the larger one, and of the larger one equal to 
     that of the smaller one.

A ball of mass m and radius r is released in a viscous liquid. The value of its terminal
velocity varies linearly with 
(1) 1/r only
(2) m/r  
(3) ${(m/r)}^{1/2}$
(4) m only 

If the work done in blowing a soap bubble of volume V is W, then the work done in
blowing a soap bubble of volume 2 V will be 
(1) W 
(2) 2 W 
(3) $\sqrt{2 W}$
(4) $W{\left(4\right)}^{1/3}$

If time period of a body depends on density (p), length (a) surface tension (S), then its
value is proportional to 
(1) $\frac{p^{1/2}{a}^{3/2}}{\sqrt{S}}$ 
(2) $\frac{p^{3/2}{a}^{3/2}}{\sqrt{S}}$
$$
(3) $\frac{p^{1/2}{a}^{3/2}}{S^{3/4}}$
(4) $\frac{p^{1/2}{a}^{1/2}}{S^{3/4}}$
 

A pump motor is used to deliver water at a certain rate from a given pipe. To obtain
twice as much water from the same pipe in the same time, power of the motor has to
be increased to
(1) 16 times
(2) 4 times
(3) 8 times
(4) 2 times


The spring balance A reads 2 kg with a block m suspended from it. A balance B reads
5 kg when a beaker with liquid is put on the pan of the balance. The two balances are
now so arranged that the hanging mass is inside the liquid in the beaker as shown in
figure. In this situation

 
(1) the balance A will read more than 2 kg
(2) the balance B will read less than 5kg
(3) the balance 4 will read less than 2kg
(4) the balance 4 and B will read 2 kg and 5 kg respectively
 

A sphere of radius R has a concentric cavity of radius r. The relative density of the material of the sphere is $\sigma$. It just floats when placed in a tank full of water. The ratio $\frac{R}{r}$is 
(1) ${\left(\frac{\sigma -1}{\sigma }\right)}^{1/3}$
(2) ${\left(\frac{\sigma }{\sigma -1}\right)}^{1/3}$
(3) ${\left(\frac{\sigma +1}{\sigma }\right)}^2$
(4) ${\left(\frac{\sigma }{\sigma +1}\right)}^3$

A cube of side 10 cm is floating between two immiscible liquids of densities 1200 kg m
${}^{-3}$ and 800 kg m${}^{-3}$ in such a way that 70% of its  volume is inside the heavier liquid.
What is the density of material of the cube 
(1) 1080 kgm${}^{-3}$ 
(2) 1040 kg m${}^{-3}$
(3) 1000 kg m${}^{-3}$
(4) 920 kg m${}^{-3}$

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 
 

A cylindrical vessel contains a liquid of density p up to a height h. The liquid is closed
by a piston of mass m and are of cross section A. There is a small hole at the bottom
of the vessel. The speed v with which the liquid comes out of the hole is: 
 

(1) $\sqrt{2 gh }$
(2) $\sqrt{2\left(gh +\frac{mg }{pA}\right)}$
(3) $\sqrt{2\left(gh+\frac{mg }{A}\right)}$
(4) $\sqrt{2 \left(gh+\frac{mg}{A}\right)}$

A liquid film is formed over a frame ABCD as shown in figure. Wire CD (mass less) can slide without friction. The mass to be hung from CD to keep it in equilibrium is (Surface tension of liquid is T)

1.  $\frac{T}{g}$ 
2.  $\frac{2Tl}{g }$
3. $\frac{g}{2Tl}$
4. \(T\times l\)$$

A raft of wood (density 600 kg/m${}^3$ of mass 120 kg floats in water. How much weight can
be put on the raft to make it just sink?
(1) 120 kg 
(2) 200 kg 
(3) 40 kg 
(4) 80 kg 

The radii of two bubbles are R${}_1$and R${}_2$ respectively. The ratio of masses of air in then will be (where T= surface tension)
(1) $\frac{R_1^{ 3}}{R_2^{ 3}}$
(2) $\frac{R_2^3}{R_1^3}$
(3) $\left(\frac{\mathrm{P} + {\displaystyle \frac{4\mathrm{T}}{{\mathrm{R}}_1}}}{\mathrm{P} + \frac{4\mathrm{T}}{{\mathrm{R}}_2}}\right)\frac{{\mathrm{R}}_1^1}{{\mathrm{R}}_2^1}$
(4) $\left(\frac{\mathrm{P} + {\displaystyle \frac{4\mathrm{T}}{{\mathrm{R}}_1}}}{\mathrm{P} + {\displaystyle \frac{4\mathrm{T}}{{\mathrm{R}}_2}}}\right)\frac{{\mathrm{R}}_2^1}{{\mathrm{R}}_1^1}$