A tube of length h (which is wide enough so that surface tension effects can be neglected) is filled with air and closed at one end is lowered into a tank of mercury to a depth h as shown; so that mercury rises a distance x into the tube. If the mercury barometer also reads 'h', then
                               

1. $\mathrm{h} (\mathrm{h}-\mathrm{x})={\mathrm{h}}^2$

2. $(2\mathrm{h}-\mathrm{x}) (\mathrm{h}-\mathrm{x})={\mathrm{h}}^2$

3. $(2\mathrm{h}-\mathrm{x}) (\mathrm{h}+\mathrm{x})={\mathrm{h}}^2$

4. $\left(2\mathrm{h}\right) (\mathrm{h}-\mathrm{x})={\mathrm{h}}^2$

A U-tube of base length I filled with same volume of two liquids of densities $\rho and 2\rho$ is moving with an acceleration a on the horizontal plane. If the height difference between the two surfaces fopen to atmosphere) becomes zero, then height h is given by

1. $\frac{al}{g}$

2. $\frac{3al}{2g}$

3. $\frac{2al}{3g}$

4. $\frac{al}{2g}$

A faulty barometer contains some air which occupies 9.5 cc. If indicates 740 mm when a correct barometer indicates 750 mm, the volume the air would occupy under standard pressure

1. 0.0.95 cc

2. 0.125 cc

3. 1.25 cc

4. 12.5 cc

A hole is made at the bottom of the tank filled with water (density= 1000 kg/m³). If the total pressure at the botton of the tand is three atmoshphere (1 atmosphere = ${10}^5$ N/m²), then the velocity of efflux is

1. $\sqrt{400} \mathrm{m}/\mathrm{s}$

2. $\sqrt{200} \mathrm{m}/\mathrm{s}$

3. $\sqrt{6400} \mathrm{m}/\mathrm{s}$

4. $\sqrt{500} \mathrm{m}/\mathrm{s}$

Kerosene oil rises up in the wick of a lantern because of

1. diffusion of the oil through the wick

2. surface tension

3. buoyant force of air

4. the gravitational pull of the wick

Three liquids of densioties d, 2d and 3d are mixed in equal proportions of weights. The relatice density of the mixture is

1. $\frac{11}{7}\mathrm{d}$

2. $\frac{18}{11}\mathrm{d}$

3. $\frac{13}{9}\mathrm{d}$

4.  $\frac{23}{18}\mathrm{d}$

 A capillary tube is dipped in a liquid. Let pressure at point A, B and C be $p_{A\text{'}} p_{B\text{'}} p_C$ respectively then

1. $p_A=p_B=p_C$

2. $p_A=p_B<p_C$

3. $p_A=p_C<p_B$

4. $p_A=p_C>p_B$

 For the arrangement shown in the figure, the force at the bottom of the vessel is

1. 200 N

2. 100 N

3. 20 N

4. 2 N

A tank is filled to a height H. The range of water coming out of a hole which is a depth H/4 from the surface of water level is

1. $\frac{2H}{\sqrt{3}}$

2. $\frac{\sqrt{3}H}{2}$

3. $\sqrt{3}H$

4. $\frac{3H}{4}$

Two rain drops falling through air have radii in the ratio 1:2. They will have terminal velocity in the ratio

1. 4:1

2. 1:4

3. 2:1

4. 1:2