When the system shown in the adjoining figure is in equilibrium and if the areas of cross section of the smaller piston and bigger piston are a and 10 a mass on smaller and bigger pistons are  m amd M, then

1. m=M

2. m= 10M

3. M= 10 m

4. M= 100 m

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 increase

4. Both l and h decrease

What is the velocity v of a metallic ball of radius r failing in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is h)

1. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-2\mathrm{\sigma })$

2. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(2\mathrm{\rho }-\mathrm{\sigma })$

3. $\frac{{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-\mathrm{\sigma })$

4. $\frac{2{\mathrm{r}}^2\mathrm{g}}{9\mathrm{\eta }}(\mathrm{\rho }-\mathrm{\sigma })$

5. $\frac{{\mathrm{r}}^2\mathrm{g}}{18\mathrm{\eta }}(\mathrm{\rho }-2\mathrm{\sigma })$

A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one pf the walls at a depth D below the surface of water. Express the horizontal distance x in terms of H and D

1. $\mathrm{x}=\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

2. $\mathrm{x}=\sqrt{\frac{\mathrm{D}(\mathrm{H}-\mathrm{D})}{2}}$

3. $\mathrm{x}=2\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

4. $\mathrm{x}=4\sqrt{\mathrm{D}(\mathrm{H}-\mathrm{D})}$

A U-tube od uniform cross section as shown in figure is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube are the same, while the level of liquid I has risen by 2cm. If the specific gravity of liquid I is 1.1 the specific gravity of liquid II must be
                        

1. 1.12

2. 1.1

3. 1.05

4. 1.0

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. $\sqrt{400}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

2. $\sqrt{200}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

3. $\sqrt{6400}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

4. $\sqrt{500}<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

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