In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is: \(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)$$

              
1. \(1200~\text{kg/m}^{3}\)
2. \(750~\text{kg/m}^{3}\)
3. \(1000~\text{kg/m}^{3}\)
4. \(1333~\text{kg/m}^{3}\)

Two small spherical metal balls, having equal masses, are made from materials of densities \(\rho_1\) and \(\rho_2\) such that ${}_{}$\(\rho_1=8\rho_2\) and having radii of \(1\) mm and \(2\) mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals \(\eta\) and whose density is \(0.1\rho_2\)${\mathrm{}}_{}$. The ratio of their terminal velocities would be:

The velocity of a small ball of mass m and density $\mathrm{\rho }$ when dropped in a container filled with glycerin of density $\sigma$ becomes constant after sometime. The viscous force acting on the ball in the final stage is:-

1. $\mathrm{mg}\left(\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

2. $\mathrm{mg}\left(1+\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

3. $\mathrm{mg}\left(1-\frac{\mathrm{\sigma }}{\mathrm{\rho }}\right)$

4. mg

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:

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. \(1.50\)