Q. No.The area of cross-section of the wider tube shown in the figure is \(800~\text{cm}^2.\) If a mass of \(12~\text{kg}\) is placed on the massless piston, then the difference in heights \(h\) of the levels of water in the two tubes will be:
1.
\(10~\text{cm}\)
2.
\(6~\text{cm}\)
3.
\(15~\text{cm}\)
4.
\(2~\text{cm}\)
The radius of a soap bubble is increased from R to 2 R. Work done in this process (T = surface tension) is:
| 1. | 24 πR2T | 2. | 48 πR2T |
| 3. | 12 πR2T | 4. | 36 πR2T |
A rectangular film of liquid is extended from \((4~\text{cm} \times2 ~\text{cm})\) to \((5 ~\text{cm}\times 4 ~\text{cm})\). If the work done is \(3 \times 10^{-4}~\text{J},\) the value of the surface tension of the liquid is:
1. \(0.25\) N/m
2. \(0.125\) N/m
3. \(0.2\) N/m
4. \(8.0\) N/m
Three liquids of densities (with ), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact 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. | \(\pi>\theta_1>\theta_2>\theta_3>\frac{\pi}{2}\) |
Two non-mixing liquids of densities and \(n 𝜌 (n>1)\) are put in a container. The height of each liquid is \(h.\) A solid cylinder floats with its axis vertical and length \(pL (𝑝 < 1)\) in the denser liquid. The density of the cylinder is \(d.\) The density \(d\) is equal to:
1. \({[2+(n+1)p}] 𝜌\)
2. \([{2+(n-1)p}] 𝜌\)
3. \([{1+(n-1)p}] 𝜌\)
4. \([{1+(n+1)p}] 𝜌\)
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. | \(\dfrac{vR^2}{n^2r^2}\) | 2. | \(\dfrac{vR^2}{nr^2}\) |
| 3. | \(\dfrac{vR^2}{n^3r^2}\) | 4. | \(\dfrac{v^2R}{nr}\) |
The heart of a man pumps 5 L of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury is \(13.6\times 10^3\)kg/m3 and g =10 m/s2, then the power of heart in watt is:
1. 1.70
2. 2.35
3. 3.0
4. 1.50
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:\(\text { Energy }=4 V T\left(\frac{1}{r}-\frac{1}{R}\right) \text { is released } \)
| 1. | Energy = \(4 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 2. | Energy =\(3 V T\left(\frac{1}{r}+\frac{1}{R}\right)\) is released |
| 3. | Energy =\(3 V T\left(\frac{1}{r}-\frac{1}{R}\right)\) is released | 4. | Energy is neither released nor absorbed |
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. \(\dfrac{1}{2} m v^{3}\)
2. \(m v^{3}\)
3. \(\dfrac{1}{2} m v^{2}\)
4. \(\dfrac{1}{2} m^{2} v^{2}\)
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