A soap bubble, having a radius of \(1~\text{mm}\), is blown from a detergent solution having a surface tension of\(2.5\times 10^{-2}~\text{N/m}\)$$. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of the water in a container. Taking \(g = 10~\text{m/s}^{2}\)${\mathrm{}}^{}$, the density of water \(= 10^{3}~\text{kg/m}^3\)${\mathrm{}}^{}$, the value of \(Z_0\) is:

1.	\(0.5~\text{cm}\)	2.	\(100~\text{cm}\)
3.	\(10~\text{cm}\)	4.	\(1~\text{cm}\)

A small hole of an area of cross-section \(2~\text{mm}^2\) is present near the bottom of a fully filled open tank of height \(2~\text{m}\). Taking \(g = 10~\text{m/s}^2\)${\mathrm{}}^{}$, the rate of flow of water through the open hole would be nearly:
1. \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\)
2. \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\)
3. \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\)
4. \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\)

A certain number of spherical drops of a liquid of radius \({r}\) coalesce to form a single drop of radius \({R}\) and volume \({V}\). If \({T}\) is the surface tension of the liquid, then:

A wind with a speed of \(40\) m/s blows parallel to the roof of a house. The area of the roof is \(250\) m². 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: (\(\rho_{\text {air }}=1.2\)${\mathrm{ }}_{}\mathrm{kg}/{\mathrm{m}}^3$)
1. \(4 \times 10^5\) N, downwards
2. \(4 \times 10^5\) N, upwards
3. \(2.4 \times 10^5\) N, upwards
4. \(2.4 \times 10^5\) N, downwards

The approximate depth of an ocean is \(2700~\text{m}\). The compressibility of water is \(45.4\times10^{-11}~\text{Pa}^{-1}\) and the density of water is \(10^{3}~\text{kg/m}^3\). What fractional compression of water will be obtained at the bottom of the ocean?
1. \(0.8\times 10^{-2}\)
2. \(1.0\times 10^{-2}\)
3. \(1.2\times 10^{-2}\)
4. \(1.4\times 10^{-2}\)

The heart of a man pumps \(5~\text{L}\) of blood through the arteries per minute at a pressure of \(150~\text{mm}\) of mercury. If the density of mercury is \(13.6\times10^{3}~\text{kg/m}^{3}\)$$ $\mathrm{and}{\mathrm{}}^{}$ \(g = 10~\text{m/s}^2\), then the power of the heart in watt is:
1. \(1.70\)
2. \(2.35\)
3. \(3.0\)
4. \(1.50\)

Water rises to height '\(h\)' in a capillary tube. If the length of capillary tube above the surface of the water is made less than \('h'\), then:

The cylindrical tube of a spray pump has a radius \(R,\) one end of which has \(n\) fine holes, each of radius \(r.\) If the speed of the liquid in the tube is \(v,\) the speed of the ejection of the liquid through the holes is:
 

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 of length \(L\) and density \(d\) is put in this container. The cylinder floats with its axis vertical and length \(rL~(r<1))\) in the denser liquid. The density \(d\) is equal to:
1. \([2+(n+1)r ]\rho\)
2. \([2+(n-1)r] \rho\)
3. \([1+(n-1)r] \rho\)
4. \([1+(n+1)r ]\rho\)