Q. No.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
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 U tube with both ends open to the atmosphere,is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is
1.
2.
3.
4.
| 1. | \(r^3\) | 2. | \(r^2\) |
| 3. | \(r^5\) | 4. | \(r^4\) |
A rectangular film of liquid is extended from \((4~\text{cm} \times 2~\text{cm})\) to \((5~\text{cm} \times 4~\text{cm}).\) If the work done is \(3\times 10^{-4}~\text J,\) then the value of the surface tension of the liquid is:
1. \(0.250~\text{Nm}^{-1}\)
2. \(0.125~\text{Nm}^{-1}\)
3. \(0.2~\text{Nm}^{-1}\)
4. \(8.0~\text{Nm}^{-1}\)
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:
| 1. | \(\dfrac{vR^{2}}{n^{2}r^{2}}\) | 2. | \(\dfrac{vR^{2}}{nr^{2}}\) |
| 3. | \(\dfrac{vR^{2}}{n^{3}r^{2}}\) | 4. | \(\dfrac{v^{2}R}{nr}\) |
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:
| 1. | water does not rise at all. |
| 2. | water rises up to the tip of capillary tube and then starts overflowing like a fountain. |
| 3. | water rises up to the top of capillary tube and stays there without overflowing. |
| 4. | water rises up to a point a little below the top and stays there. |
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 \(13.6\times10^{3}~\text{kg/m}^{3}\) \(g = 10~\text{m/s}^2,\) then the power of the heart in watts is:
| 1. | \(1.70\) | 2. | \(2.35\) |
| 3. | \(3.0\) | 4. | \(1.50\) |
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. \(1.4\times 10^{-2}\)
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