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A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity $\omega$ then.
                                
 
1.  water levels in both sections A and B go up
2.  water level in section A goes up and that in B comes down
3.  water level in section A comes down and that in B it goes up
4.  water levels remain the same in both sections

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg $(\mathrm{density} = 13.6 \mathrm{gm}/{\mathrm{cm}}^3).$ Using the straw, he can drink water from a glass up to a maximum depth of :
1.  10 cm 
2.  75 cm
3.  13.6 cm 
4.  1.36 cm

$\mathrm{Work} \mathrm{of} 3.0 \times {10}^{–4} \mathrm{joules} \mathrm{is} \mathrm{required} \mathrm{to} \mathrm{be} \mathrm{done} \mathrm{in} \mathrm{increasing} \mathrm{the} \mathrm{size} \mathrm{of} \mathrm{a} \mathrm{soap} \mathrm{film} \mathrm{from} 10 \mathrm{cm} \times 6 \mathrm{cm} \mathrm{to} 10 \mathrm{cm} \times 11 \mathrm{cm}. \mathrm{The} \mathrm{surface}$
$\mathrm{tension} \mathrm{of} \mathrm{the} \mathrm{film} \mathrm{is}$
1.  $5 \times {10}^{–2} \mathrm{N}/\mathrm{m}$
2.  $3 \times {10}^{–2} \mathrm{N}/\mathrm{m}$
3.  $1.5 \times {10}^{–2} \mathrm{N}/\mathrm{m}$ 
4.  $1.2 \times {10}^{–2} \mathrm{N}/\mathrm{m}$

If the terminal speed of a sphere of gold $(\mathrm{density} = 19.5 \mathrm{kg}/{\mathrm{m}}^3)$ is 0.2 m/s in a viscous liquid $(\mathrm{density} = 1.5 \mathrm{kg}/{\mathrm{m}}^3),$ find the terminal speed of a sphere of silver $(\mathrm{density} = 10.5 \mathrm{kg}/{\mathrm{m}}^3)$ of the same size in the same liquid
1.  0.4 m/s 
2.  0.133 m/s
3.  0.1 m/s 
4.  0.2 m/s

Water is filled in a container up to a height of 3m. A small hole of the area $‘A_0’$ is punched in the wall of the container at a height 52.5 cm from the bottom. The cross-sectional area of the container is A. If ${\mathrm{A}}_{0 }/\mathrm{A} = 0.1$ then ${\mathrm{v}}^2$ is (where v is the velocity of water coming out of the hole) 
 
1.  $50 {\mathrm{m}}^2/{\mathrm{s}}^2$
2.  $50 .5 {\mathrm{m}}^2/{\mathrm{s}}^2$
3.  $51 {\mathrm{m}}^2/{\mathrm{s}}^2$
4.  $52 {\mathrm{m}}^2/{\mathrm{s}}^2$

A boy has 60 kg weight. He wants to swim in a river with the help of a wooden log. If the relative density of wood is 0.6, what is the minimum volume of the wooden log?  $(\mathrm{density} \mathrm{of} \mathrm{river} \mathrm{water} \mathrm{is} 1000 \mathrm{kg}/{\mathrm{m}}^3)$

1.  $0.66 {\mathrm{m}}^3$
2.  $150 {\mathrm{m}}^3$
3.  $\frac{3}{1} {\mathrm{m}}^3$
4.  $\frac{3}{20} {\mathrm{m}}^3$

The work is done in blowing a soap bubble of radius 0.2m, given that the surface tension of soap solution is $60 \times {10}^{–3} \mathrm{N}/\mathrm{M}$ is:
1.  $24\mathrm{\pi } \times {10}^{–4}\mathrm{J}$
2.  $24\mathrm{\pi } \times {10}^{–4}\mathrm{J}$
3.  $96\mathrm{\pi } \times {10}^{–4}\mathrm{J}$
4.  $1.92\mathrm{\pi } \times {10}^{–4}\mathrm{J}$

Water rises to a height of 10 cm in a capillary tube and the mercury falls to a depth of 3.1 cm in the same capillary tube. If the density of mercury is 13.6 and the angle of contact for mercury is 135°, the approximate ratio of surface tensions of water and mercury is
1.  1 : 0.15 
2.  1 : 3
3.  1 : 6 
4.  1.5 : 1

The lift of an airplane is based on 
1.  Torricelli's theorem
2.  Bernoulli's theorem
3.  Law of gravitation
4.  Conservation of linear momentum.

$\mathrm{A} \mathrm{spherical} \mathrm{solid} \mathrm{ball} \mathrm{of} \mathrm{volume} \mathrm{V} \mathrm{is} \mathrm{made} \mathrm{of} \mathrm{a} \mathrm{material} \mathrm{of} \mathrm{density} {\mathrm{\rho }}_1. \mathrm{It} \mathrm{is} \mathrm{falling} \mathrm{through} \mathrm{a} \mathrm{liquid} \mathrm{of} \mathrm{density} {\mathrm{\rho }}_1 ({\mathrm{\rho }}_2 < {\mathrm{\rho }}_1). \mathrm{Assume} \mathrm{that} \mathrm{the}$
$\mathrm{liquid} \mathrm{applies} \mathrm{a} \mathrm{viscous} \mathrm{force} \mathrm{on} \mathrm{the} \mathrm{ball} \mathrm{that} \mathrm{is} \mathrm{proportional} \mathrm{to} \mathrm{the} \mathrm{square} \mathrm{of} \mathrm{its} \mathrm{speed} \mathrm{v}, \mathrm{i}.\mathrm{e}., {\mathrm{F}}_{\mathrm{viscous}} = –{\mathrm{kv}}^2 (\mathrm{k} > 0). \mathrm{The} \mathrm{terminal}$
$\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{ball} \mathrm{is}$
1.  $\sqrt{\frac{\mathrm{Vg}\left({\mathrm{\rho }}_1 - {\mathrm{\rho }}_2\right)}{\mathrm{k}}}$
2.  $\frac{{\mathrm{Vg\rho }}_1}{\mathrm{k}}$
3.  $\sqrt{\frac{{\mathrm{Vg\rho }}_1}{\mathrm{k}}}$
4.  $\frac{\mathrm{Vg}\left({\mathrm{\rho }}_1 - {\mathrm{\rho }}_2\right)}{\mathrm{k}}$

A ring is cut from a platinum tube 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from the pan of a balance, so that it comes in contact with the water in a glass vessel. If an extra 3.97. It is required to pull it away from water, the surface tension of water is
1.  $72 \mathrm{dyne} {\mathrm{cm}}^{–1}$
2.  70.80 dyne ${\mathrm{cm}}^{–1}$
3.  63.35 dyne ${\mathrm{cm}}^{–1}$
4.  60 dyne ${\mathrm{cm}}^{–1}$

A water tank of height 10m, completely filled with water is placed on level ground. It has two holes one at 3 m and the other at 7 m from its base. The water ejecting from 
1.  both the holes will fall at the same spot
2.  upper hole will fall farther than that from the lower hole
3.  upper hole will fall closer than that from the lower hole
4.  more information is required

Which of the following relation is true?
1.  $3\mathrm{Y} = \mathrm{k}\left(1 - \mathrm{\sigma }\right)$
2.  $\mathrm{K} = \frac{9\mathrm{\eta Y}}{\mathrm{Y} + \mathrm{\eta }}$
3.  $\mathrm{\sigma } = \left(6\mathrm{K} + \mathrm{\eta }\right)\mathrm{Y}$
4.  $\mathrm{\sigma } = \frac{0.5 \mathrm{Y} - \mathrm{\eta }}{\mathrm{\eta }}$

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 increases
4.  both $l$ and h decreases

$1 {\mathrm{m}}^3$ water is brought inside the lake up to 200 metres depth from the surface of the lake. What will be changed in the volume when the bulk modulus of elastically of water is 22000 atmosphere? 
$(\mathrm{density} \mathrm{of} \mathrm{water} \mathrm{is} 1 \times {10}^3 \mathrm{kg}/{\mathrm{m}}^3 \mathrm{atmosphere} \mathrm{pressure} = {10}^{5 }\mathrm{N}/{\mathrm{m}}^2 \mathrm{and} \mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2 )$
1.  8.9 × ${10}^{–3} {\mathrm{m}}^3$
2.  7.8 × ${10}^{–3} {\mathrm{m}}^3$
3.  9.1 × ${10}^{–4 }{\mathrm{m}}^3$
4.  8.7 × ${10}^{–4 }{\mathrm{m}}^3$

The excess of pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
1.  0.125 
2.  0.250
3.  1 
4.  2

A steel wire is suspended vertically from a rigid support. When loaded with a weight in the air, it extends by $l_a$ and when the weight is immersed completely in water, the extension is reduced to $l_w.$ Then the relative density of the material of the weight is
1.  $\frac{l_a}{l_w}$
2.   $\frac{l_a}{l_a - l_w}$
3.  $\frac{l_w}{\left(l_a - l_w\right)}$
4.  $\frac{l_w}{l_a}$

Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is r, the surface tension of water is T and the atmospheric pressure is ${\mathrm{P}}_0.$ Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on the water on one side of this section by water on the other side of this section has a magnitude
                                                                  
1.  $\left|2P_{0}Rh + {\mathrm{\pi R}}^2\mathrm{\rho gh} - 2\mathrm{RT}\right|$
2.  $\left|2P_{0}Rh + R{\mathrm{\rho gh}}^2 - 2\mathrm{RT}\right|$
3.  $\left|P_0\pi R^2 + R{\mathrm{\rho gh}}^2 - 2\mathrm{RT}\right|$
4.  $\left|P_0\pi R^2 + {\mathrm{R\rho gh}}^2 + 2\mathrm{RT}\right|$

A vessel contains oil $(\mathrm{density} = 0.8 \mathrm{gm}/{\mathrm{cm}}^3)$ over mercury $(\mathrm{density} = 13.6 \mathrm{gm}/{\mathrm{cm}}^3).$ A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $\mathrm{gm}/{\mathrm{cm}}^3$ is 
1.  3.3 
2.  6.4
3.  7.2 
4.  12.8

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half-submerged in a liquid of density $\sigma$ at the equilibrium position. The extension ${\mathrm{X}}_0$ of the spring when it is in equilibrium is:
1.  $\frac{\mathrm{Mg}}{\mathrm{k}}$
2.  $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1 - \frac{\mathrm{LA\sigma }}{\mathrm{M}}\right)$
3.  $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1 - \frac{\mathrm{LA\sigma }}{2\mathrm{M}}\right)$
4.  $\frac{\mathrm{Mg}}{\mathrm{k}}\left(1 - \frac{\mathrm{LA\sigma }}{\mathrm{M}}\right)$

If two glass plates have water between them and are separated by a very small distance (see figure), it is very difficult to pull them apart. It is because of the water in between forms cylindrical surfaces on the side that gives rise to lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is R and the surface tension of water is T then the pressure in water between the plates is lower by
                         
1.  $\frac{2\mathrm{T}}{\mathrm{R}}$
2.  $\frac{4\mathrm{T}}{\mathrm{R}}$
3.  $\frac{\mathrm{T}}{4\mathrm{R}}$
4.  $\frac{\mathrm{T}}{\mathrm{R}}$