The area of cross-section of the wider tube shown in the figure is $800$ ${\mathrm{cm}}^2.$ If a mass of 12 kg is placed on the massless piston, then the difference in heights h of the levels of water in the two tubes will be:

    

1.	10 cm	2.	6 cm
3.	15 cm	4.	2 cm

 Two non-mixing liquids of densities $\rho$ and n$\rho$(n>1) are put in a container. The height of each liquid is h. A solid cylinder  floats with its axis vertical and length pL $\left(p<1\right)$ in the denser liquid. The density of the cylinder is d. The density d is equal to:

1. {2+(n+1)p}$\rho$             

2. {2+(n-1)p}$\rho$

3. {1+(n-1)p}$\rho$             

4. {1+(n+1)p}$\rho$

A wind with speed \(40~\text{m/s}\) blows parallel to the roof of a house. The area of the roof is \(250~\text{m}^2\). Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be: \(\left(\rho_{\text{air}}= 1.2~\text{kg/m}^3 \right)\)
1. \(4.8\times 10^{5}~\text{N}, ~\text{downwards}\)
2. \(4.8\times 10^{5}~\text{N}, ~\text{upwards}\)
3. \(2.4\times 10^{5}~\text{N}, ~\text{upwards}\)
4. \(2.4\times 10^{5}~\text{N}, ~\text{downwards}\)

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is v, then the speed of ejection of the liquid through the holes will be:
1. vR²/n²r²

2. vR²/nr²

3. vR²/n³r²

4. v²R/nr

An engine pumps water continuously through a hose. Water leaves the hose with a velocity \(v\) and \(m\) is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1. $\frac{1}{2}m{v}^3$                                   

2. $m{v}^3$

3. $\frac{1}{2}m{v}^2$                                   

4. $\frac{1}{2}{m}^2{v}^2$

Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is \(36\) g and its density is \(9\) g/cm³. If the mass of the other is \(48\) g, its density in g/cm³ will be:
1. $\frac{4}{3}$                                         

2. $\frac{3}{2}$

3. \(3\)                                           

4. \(5\)

A vertical U-tube of uniform inner cross section, contains mercury in both its arms. A glycerin (density = 1.3 g/${\mathrm{cm}}^3$) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/${\mathrm{cm}}^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are at the same horizontal level. Find the length of the oil column. [Density of mercury = 13.6 g/${\mathrm{cm}}^3$]  
                       
1. 10.4 cm
2. 8.2 cm
3. 7.2 cm
4. 9.6 cm

An iceberg of density 900 kg/${\mathrm{m}}^3$ is floating in water of density 1000 Kg/${\mathrm{m}}^3$. The percentage of volume of ice-cube outside the water is: 
1. 20%                                       
2. 35%
3. 10%                                       
4. 25%

A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?

A candle of diameter d is floating on a liquid in a cylindrical container of diameter D (D>>d) as shown in figure. If it is burning at the rate of 2cm/hour then the top of the candle will: