Q. No.(Given density of water = \(10^3 ~\text{kgm}^{-3},~ g=10 ~\text{ms}^{-2} \) and \(1~\text{atm} = 10^5~\text{Pa}\))
| 1. | \(1~\text{atm}\) | 2. | \(2~\text{atm}\) |
| 3. | \(3~\text{atm}\) | 4. | \(4~\text{atm}\) |
| 1. | pressure on the base area of vessels \(A\) and \(B\) is the same. |
| 2. | pressure on the base area of vessels \(A\) and \(B\) is not the same. |
| 3. | both vessels \(A\) and \(B\) weigh the same. |
| 4. | vessel \(B\) weighs twice that of \(A\). |
In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are \(15~\text{cm}\) and \(20~\text{cm}\) respectively. The density of the oil is:
\(\left[\text{take}~\rho_{\text{water}}= 1000~\text{kg/m}^{3}\right]\)
| 1. | \(1200~\text{kg/m}^{3}\) | 2. | \(750~\text{kg/m}^{3}\) |
| 3. | \(1000~\text{kg/m}^{3}\) | 4. | \(1333~\text{kg/m}^{3}\) |
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. | \(1.50\) |
| 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:
| 1. | \(\dfrac{vR^{2}}{n^{2}r^{2}}\) | 2. | \(\dfrac{vR^{2}}{nr^{2}}\) |
| 3. | \(\dfrac{vR^{2}}{n^{3}r^{2}}\) | 4. | \(\dfrac{v^{2}R}{nr}\) |
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. |
| 1. | \(K_1=K_2\) | 2. | \({2K}_1={K}_2\) |
| 3. | \({K}_1>{K}_2\) | 4. | \({K}_1<{K}_2\) |
A fluid of density \(\rho~\)is flowing in a pipe of varying cross-sectional area as shown in the figure. Bernoulli's equation for the motion becomes:
| 1. | \(p+\dfrac12\rho v^2+\rho gh\text{ = constant}\) | 2. | \(p+\dfrac12\rho v^2\text{ = constant}\) |
| 3. | \(\dfrac12\rho v^2+\rho gh\text{ = constant}\) | 4. | \(p+\rho gh\text{ = constant}\) |
| 1. | \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\) | 2. | \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\) |
| 3. | \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\) | 4. | \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\) |
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