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Q. No.Two non-mixing liquids of densities \(\rho\) and \(n\rho\) \((n>1)\) are put in a container. The height of each liquid is \(h.\) A solid cylinder of length \(L\) and density \(d\) is put in this container. The cylinder floats with its axis vertical and length \(rL~(r<1))\) in the denser liquid. The density \(d\) is equal to:
| 1. | \([2+(n+1)r ]\rho\) | 2. | \([2+(n-1)r] \rho\) |
| 3. | \([1+(n-1)r] \rho\) | 4. | \([1+(n+1)r ]\rho\) |
Subtopic: Â Archimedes' Principle |
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Level 2: 60%+
NEET - 2016
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When a man sits on a boat of length \(2 ~\text m\) and breadth \(1~\text m\) floating on a lake, the boat sinks by \(2~\text{cm}.\) The mass of the man is:
1. \(25~\text{kg}\)
2. \(40~\text{kg}\)
3. \(60~\text{kg}\)
4. \(80~\text{kg}\)
1. \(25~\text{kg}\)
2. \(40~\text{kg}\)
3. \(60~\text{kg}\)
4. \(80~\text{kg}\)
Subtopic: Â Archimedes' Principle |
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A boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one, how will it affect the level of water?
| 1. | It will remain unchanged |
| 2. | It will rise |
| 3. | It will fall |
| 4. | First it will first rise and then fall |
Subtopic: Â Archimedes' Principle |
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A block weighs \(5 ~\text N\) in the air and \(4.5 ~\text N\) in a liquid of specific gravity \(0.5.\) Its weight in water will be:
1. \(3.5 ~\text N\)
2. \(4.0 ~\text N\)
3. \(2.5 ~\text N\)
4. \(3.0 ~\text N\)
1. \(3.5 ~\text N\)
2. \(4.0 ~\text N\)
3. \(2.5 ~\text N\)
4. \(3.0 ~\text N\)
Subtopic: Â Archimedes' Principle |
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A candle of diameter \(d\) is floating on a liquid in a cylindrical container of diameter \(D(D>>d)\) as shown in the figure. If it is burning at the rate of \(2~\text{cm/hour}\) then the top of the candle will:
| 1. | Remain at the same height |
| 2. | Fall at the rate of \(1~\text{cm/hour}\) |
| 3. | Fall at the rate of \(2~\text{cm/hour}\) |
| 4. | Go up at the rate of \(1~\text{cm/hour}\) |
Subtopic: Â Archimedes' Principle |
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Given below are two statements:
| Statement I: | Two bodies of different masses, shapes, and sizes may experience the same thrust when their volumes inside a fluid are equal. |
| Statement II: | A soft plastic bag weighs the same when empty or when filled with air at atmospheric pressure. |
| 1. | Only Statement I is True. |
| 2. | Only Statement II is True. |
| 3. | Both Statement I and Statement II are True. |
| 4. | Both Statement I and Statement II are False. |
Subtopic: Â Archimedes' Principle |
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A solid wooden cube has sides of length \(a.\) The density of the wood is \(\rho.\) The cube is completely immersed in a beaker of oil, which has a density of \(\sigma.\) The top surface of the cube is horizontal. The gravitational field strength is \(g.\) What is the upward force (upthrust) on the cube due to the oil?
(Assume that no oil is absorbed by the wood.)
1. \((\sigma-\rho)a^{3}g\)
2. \(\rho a^{3}g\)
3. \(\sigma a^{3}\)
4. \(\sigma a^{3}g\)
(Assume that no oil is absorbed by the wood.)
1. \((\sigma-\rho)a^{3}g\)
2. \(\rho a^{3}g\)
3. \(\sigma a^{3}\)
4. \(\sigma a^{3}g\)
Subtopic: Â Archimedes' Principle |
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A small sphere of density \(\rho\) is completely submerged in a liquid of density \(3\rho\) and released. The magnitude of its acceleration just after release equals:
1. \(g\)
2. \(\dfrac{g}{3}\)
3. \(2g\)
4. \(3g\)
1. \(g\)
2. \(\dfrac{g}{3}\)
3. \(2g\)
4. \(3g\)
Subtopic: Â Archimedes' Principle |
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