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. \([1+(n+1)r ]\rho\)

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:
 

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

Three liquids of densities \(\rho_1,\rho_2\) and \(\rho_3\) \((\rho_1>\rho_2>\rho_3)\) having the same value of surface tension \(T\), rise to the same height in three identical capillaries. The angles of contact $\mathrm{}$\(\theta_1\), $\mathrm{}$\(\theta_2\)_, and $\mathrm{}$\(\theta_3\) obey:
1. \( \frac{\pi}{2}>\theta_1>\theta_2>\theta_3 \geq 0 \)
2. \( 0 \leq \theta_1<\theta_2<\theta_3<\frac{\pi}{2} \)
3. \( \frac{\pi}{2}<\theta_1<\theta_2<\theta_3<\pi \)
4. \( \pi>\theta_1>\theta_2>\theta_3>\frac{\pi}{2} \)

A capillary tube of radius \(r\) is immersed in water and water rises in it to a height \(h.\) The mass of the water in the capillary is \(5\) g. Another capillary tube of radius \(2r\) is immersed in water. The mass of water that will rise in this tube is:
1. \(5.0\) g
2. \(10.0\) g
3. \(20.0\) g
4. \(2.5\) g

Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density \(984~\text{kg/m}^3.\) The height of the wine column for normal atmospheric pressure is:
1. \(11.5~\text{m}\)
2. \(10.5~\text{m}\)
3. \(9.00~\text{m}\)
4. \(15.0~\text{m}\)

A hydraulic automobile lift is designed to lift cars with a maximum mass of \(3000\) kg. The area of the cross-section of the piston carrying the load is \(425\) cm². What maximum pressure would the smaller piston have to bear?
1. \(3.12\times10^{5}\) Pa
2. \(1.01\times10^{5}\) Pa
3. \(2.94\times10^{5}\) Pa
4. \(6.92\times10^{5}\) Pa

A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity \((v)\) of the pebble as a function of time \((t).\)
 

1.		2.
3.		4.

Which of the following diagrams does not represent a streamline flow?
 

1.		2.
3.		4.

An ideal fluid flows through a pipe of circular cross-section made of two sections with diameters \(2.5\) cm and \(3.75\) cm. The ratio of the velocities in the two pipes is:
1. \(9:4\)
2. \(3:2\)
3. \(\sqrt{3}:\sqrt{2}\)
4. \(\sqrt{2}:\sqrt{3}\)