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Q. No.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. \(1.4\times 10^{-2}\)
A wind with a speed of \(40~\text{m/s}\) 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:
\((\rho_{\text {air }}=1.2~\text{kg/m}^3)\)
1. \(4 \times 10^5~\text N,\) downwards
2. \(4 \times 10^5~\text N,\) upwards
3. \(2.4 \times 10^5~\text N,\) upwards
4. \(2.4 \times 10^5~\text N,\) downwards
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:
| 1. | the energy \(= 4{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)\) is released. |
| 2. | the energy \(={ 3{VT}\left( \frac{1}{{r}} + \frac{1}{{R}}\right)}\) is released. |
| 3. | the energy \(={ 3{VT}\left( \frac{1}{{r}} - \frac{1}{{R}}\right)}\) is released. |
| 4. | the energy is neither released nor absorbed. |
| 1. | surface tension. |
| 2. | density. |
| 3. | angle of contact between the surface and the liquid. |
| 4. | viscosity. |
The fluid is in streamlined flow through a horizontal pipe with a variable cross-sectional area. Which of the following statements is correct?
| 1. | The velocity is maximum at the narrowest part of the pipe, and pressure is maximum at the widest part of the pipe. |
| 2. | Both the velocity and pressure are maximum at the narrowest part of the pipe. |
| 3. | Both the velocity and pressure are maximum at the widest part of the pipe. |
| 4. | The velocity is minimum at the narrowest part of the pipe, and the pressure is minimum at the widest part of the pipe. |
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