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In the figure shown water is filled in a symmetrical container. Four pistons of equal area A are used at the four opening to keep the water in equilibrium. Now an additional force F is applied at each piston. The increase in the pressure at the centre of the container due to this addition is
                               
1.  $\frac{\mathrm{F}}{\mathrm{A}}$
2.  $\frac{2\mathrm{F}}{\mathrm{A}}$
3.  $\frac{4\mathrm{F}}{\mathrm{A}}$
4.  $0$

Two vessels A and B of different shapes have the same base area and are filled with water up to the same height h (see figure). The force exerted by water on the base is ${\mathrm{F}}_{\mathrm{A}}$ for vessel A and ${\mathrm{F}}_{\mathrm{B}}$ for vessel B. The respective weights of the water filled in vessels are ${\mathrm{W}}_{\mathrm{A}}$ and ${\mathrm{W}}_{\mathrm{B}}$. Then

1.  ${\mathrm{F}}_{\mathrm{A}}>{\mathrm{F}}_{\mathrm{B}} ; {\mathrm{W}}_{\mathrm{A}}>{\mathrm{W}}_{\mathrm{B}}$
2.  ${\mathrm{F}}_{\mathrm{A}}={\mathrm{F}}_{\mathrm{B}} ; {\mathrm{W}}_{\mathrm{A}}>{\mathrm{W}}_{\mathrm{B}}$
3.  ${\mathrm{F}}_{\mathrm{A}}={\mathrm{F}}_{\mathrm{B}} ; {\mathrm{W}}_{\mathrm{A}}<{\mathrm{W}}_{\mathrm{B}}$
4.  ${\mathrm{F}}_{\mathrm{A}}>{\mathrm{F}}_{\mathrm{B}} ; {\mathrm{W}}_{\mathrm{A}}={\mathrm{W}}_{\mathrm{B}}$

The density of ice is x gm/cc and that of water is y gm/cc. What is the change in volume in cc, when m gm of ice melts?
1.  M(y-x)
2.  (y-x)/m
3.  mxy(x-y)
4.  m(1/y-1/x)

Two identical cylindrical vessels with their bases at the same level, contain same liquid of density $\mathrm{\rho }$. The height of the liquid in one vessel is ${\mathrm{h}}_1$ and that in the other vessel is ${\mathrm{h}}_2$. The area of either base is A. The work done by gravity in equalizing the levels when the two vessels are connected is:
1.  $\left({\mathrm{h}}_1-{\mathrm{h}}_2\right)\mathrm{g\rho }$
2.  $\left({\mathrm{h}}_1-{\mathrm{h}}_2\right)\mathrm{g} \mathrm{A\rho }$
3.  $\frac{1}{2}{\left({\mathrm{h}}_1-{\mathrm{h}}_2\right)}^2 \mathrm{g\rho }$
4.  $\frac{1}{4}{\left({\mathrm{h}}_1-{\mathrm{h}}_2\right)}^2\mathrm{g} \mathrm{A\rho }$

A small ball of density $\mathrm{\rho }$ is immersed in a liquid of density $\mathrm{\sigma }\left(\mathrm{\sigma }>\mathrm{\rho }\right)$ to a depth h and released. The height above the surface of water up to which the ball will jump is:
1.  $\frac{\mathrm{\sigma h}}{\mathrm{\rho }}$
2.  $\left(\frac{\mathrm{\sigma }}{\mathrm{\rho }}-1\right)\mathrm{h}$
3.  $\left(1-\frac{\mathrm{\rho }}{\mathrm{\sigma }}\right)\mathrm{h}$
4.  $\frac{\mathrm{\rho h}}{\mathrm{\sigma }}$

The area of cross-section of the wider tube shown in the figure is 800 cm². If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is:
                              
1.  10 cm
2.  6 cm
3.  15 cm
4.  2 cm

An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was
1.  g/3
2.  2g/3
3.  3g/2
4.  None

An open-ended U-tube of uniform cross-sectional area contains water (density1.0 gram/centimeter³) standing initially 20 centimeters from the bottom in each arm. An immiscible liquid of density 4.0 grams/centimeter³ is added to one arm until a layer 5 centimeters high forms, as shown in the figure above. What is the ratio h2/h1 of the heights of the liquid in the two arms?
                           
1.  3/1
2.  5/2
3.  2/1
4.  3/2

A cylindrical block of area of cross-section A and of material of density $\mathrm{\rho }$ is placed in a liquid of density one-third of block. The block compresses a spring and compression in the spring is one-third of the length of the block. If acceleration due to gravity is g, the spring constant of the soring is:
                            
1.  $\mathrm{\rho Ag}$
2.  $2\mathrm{\rho Ag}$
3.  $2\mathrm{\rho Ag}/3$
4.  $\mathrm{\rho Ag}/3$

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

A horizontal pipe line carries water in a streamline flow. At a point along the pipe where cross-sectional area is 10 cm², the velocity of water is 1 m/s and pressure is 2000 Pa. The pressure of water at another point where cross-sectional area is 5 cm², is: (Density of water=1000 kg/m³)
1.  250 Pa
2.  500 Pa
3.  1000 Pa
4.  2000 Pa

A tank is filled with water up to height H. Water is allowed to come out of a hole P in one of the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D:
1.  $\mathrm{x}=\sqrt{\mathrm{D}\left(\mathrm{H}-\mathrm{D}\right)}$
2.  $\mathrm{x}=\sqrt{\frac{\mathrm{D}\left(\mathrm{H}-\mathrm{D}\right)}{2}}$
3.  $\mathrm{x}=2\sqrt{\mathrm{D}\left(\mathrm{H}-\mathrm{D}\right)}$
4.  $\mathrm{x}=4\sqrt{\mathrm{D}\left(\mathrm{H}-\mathrm{D}\right)}$

A cubical box of wine has a small spout located in one of the bottom corners. When the box is full and placed on a level surface, opening the spout results in a flow of wine with an initial speed of v₀ (see figure). When the box is half empty, someone tilts it at 45$°$ so that the spout is at the lowest point (see figure). When the spout is opened the wine will flow out with a speed of
                                  
1.  ${\mathrm{v}}_0$
2.  ${\mathrm{v}}_0/2$
3.  ${\mathrm{v}}_0/\sqrt{2}$
4.  ${\mathrm{v}}_0/\sqrt[4]{2}$

For a fluid which is flowing steadily, the level in the vertical tubes is best represented by
1.                              
2.  
3.                             
4.  

Overall changes in volume and radius of a uniform cylindrical steel wire are \(0.2\%\) and \(0.002\%\) respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is: \(\left(2.0\times 10^{11}~\text{Nm}^{-2}\right)\)
1. \(3.2\times 10^{11}~\text{Nm}^{-2}\)
2. \(3.2\times 10^{7}~\text{Nm}^{-2}\)
3. \(3.6\times 10^{9}~\text{Nm}^{-2}\)
4. \(3.9\times 10^{8}~\text{Nm}^{-2}\)

A solid sphere of radius R made of material of bulk modules K is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, the fractional change in the radius of the sphere $\mathrm{\delta R}/\mathrm{R}$is
1.  mg/AK
2.  mg/3AK
3.  mg/A
4.  mg/3AR

A cylindrical wire of radius 1 mm, length 1m, Young's modulus $=2\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$, poisson's ratio $\mathrm{\mu }=\mathrm{\pi }/10$ is stretched by a force of 100 N. Its radius will become?
1.  0.99998 mm
2.  0.99999 mm
3.  0.99997 mm
4.  0.99995 mm

A uniform rod rotating in gravity free region with certain constant angular velocity. The variation of tensile stress with distance x from axis of rotation is best represented by which of the following graphs.
1.                                  2.  
3.                                  4.  

The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line
                                                               
1.  OB
2.  OA
3.  OD
4.  OC