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Q. No.Two copper vessels \(A\) and \(B\) have the same base area but are of different shapes. \(A\) takes twice the volume of water that \(B\) requires to fill up to a particular common height. Then the correct statement among the following is:
1. pressure on the base area of vessels \(A\) and \(B\) is same.
2. pressure on the base area of vessels \(A\) and \(B\) is not same.
3. both vessels \(A\) and \(B\) weigh the same.
4. vessel \(B\) weighs twice that of \(A\).
Subtopic: Pressure |
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The terminal velocity of a copper ball of radius \(5~\text{mm}\) falling through a tank of oil at room temperature is \(10~\text{cm}~\text{s}^{-1}\) . If the viscosity of oil at room temperature is \(0.9~\text{kg}~\text{m}^{-1}~\text{s}^{-1}\), the viscous drag force is:
1. \(8.48 \times10^{-3}\) N
2. \(8.48 \times10^{-5}\) N
3. \(4.23 \times10^{-3}\) N
4. \(4.23 \times10^{-6}\) N
1. \(8.48 \times10^{-3}\) N
2. \(8.48 \times10^{-5}\) N
3. \(4.23 \times10^{-3}\) N
4. \(4.23 \times10^{-6}\) N
Subtopic: Stokes' Law |
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Given below are two statements:
| Statement I: | The pressure at the bottom of a vessel containing water is proportional to the height of the water. |
| Statement II: | When water begins to flow out of a small hole in a tank (after the hole is opened), the pressure of water inside the tank near the hole decreases. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Pressure |
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Water flows from a small hole at the bottom of a rectangular tank at \(10\) m/s after it had been filled for \(20\) min. For how much time should the empty tank be filled at the same rate so that the speed of efflux is doubled? (i.e. it becomes \(20\) m/s)
1. \(40\) min
2. \(80\) min
3. \(160\) min
4. \(320\) min
1. \(40\) min
2. \(80\) min
3. \(160\) min
4. \(320\) min
Subtopic: Bernoulli's Theorem |
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Air is pushed carefully into a soap bubble of radius \(r\) to double its radius. If the surface tension of the soap solution is \(T,\) then work done in the process is:
| 1. | \(12\pi r^2T\) | 2. | \(24\pi r^2T\) |
| 3. | \(4\pi r^2T\) | 4. | \(8\pi r^2T\) |
Subtopic: Surface Tension |
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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. \(p+\frac12\rho v^2+\rho gh\text{=constant}\)
2. \(p+\frac12\rho v^2\text{=constant}\)
3. \(\frac12\rho v^2+\rho gh\text{=constant}\)
4. \(p+\rho gh\text{=constant}\)
Subtopic: Bernoulli's Theorem |
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The correct statement about the variation of viscosity of fluids with an increase in temperature is:
| 1. | viscosity of gases decreases. |
| 2. | viscosity of both liquids and gases increases. |
| 3. | viscosity of liquids increases. |
| 4. | viscosity of liquids decreases. |
Subtopic: Viscosity |
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If a soap bubble expands, the pressure inside the bubble:
| 1. | is equal to the atmospheric pressure | 2. | decreases |
| 3. | increases | 4. | remains the same |
Subtopic: Surface Tension |
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A tank full of water is placed in an elevator. The elevator accelerates upward. The water pressure at the bottom of the tank:
| 1. | decreases |
| 2. | increases |
| 3. | remains unchanged |
| 4. | first increases and then decreases |
Subtopic: Pressure |
77%
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When water flows out of a small hole at the bottom of a large tank of uniform cross-section, the average flow rate equals the average of the initial and the final flow rate. The time to empty the tank is \(1\) hr, using a small pipe at the bottom. If the tank were to be filled to twice its previous level, the time required will be:
1. \(1\) hr
2. \(\sqrt2\) hr
3. \(2\) hr
4. \(4\) hr
1. \(1\) hr
2. \(\sqrt2\) hr
3. \(2\) hr
4. \(4\) hr
Subtopic: Bernoulli's Theorem |
74%
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