Q. No.The area of cross-section of the wider tube shown in the figure is 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
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 cm ) to \((4 ~\text{cm}\times 5 ~\text{cm})\). If the work done is J, the value of the surface tension of the liquid is:
| 1. | 0.250 Nm-1 | 2. | 0.125 Nm-1 |
| 3. | 0.2 Nm-1 | 4. | 8.0 Nm-1 |
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(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 in the denser liquid. The density of the cylinder is d. The density d is equal to:
1. {2+(n+1)p}
2. {2+(n-1)p}
3. {1+(n-1)p}
4. {1+(n+1)p}
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
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?
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2.
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4.
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