- 1(current)
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. \([1+(n+1)r ]\rho\)
1. \(25~\text{kg}\)
2. \(40~\text{kg}\)
3. \(60~\text{kg}\)
4. \(80~\text{kg}\)
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 |
1. \(3.5 ~\text N\)
2. \(4.0 ~\text N\)
3. \(2.5 ~\text N\)
4. \(3.0 ~\text N\)
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 \(1~\text{cm/hour}\) |
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. |
(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. \(\sigma a^{3}g\)
1. \(g\)
2. \(\dfrac{g}{3}\)
3. \(2g\)
4. \(3g\)
- 1(current)
Q. No.
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