Q. No.(take \(g=10~\text{m/s}^2,\) density of water \(=1000~\text{kg/m}^3\))
1. \(3 \times 10^6 ~\text{kg}~\text{m}^{-1}~ \text{s}^{-2}\)
2. \(3 \times 10^7 ~\text{kg}~\text{m}^{-1}~ \text{s}^{-2}\)
3. \(3 \times 10^8 ~\text{kg}~\text{m}^{-1}~ \text{s}^{-2}\)
4. \(3 \times 10^9 ~\text{kg}~\text{m}^{-1}~ \text{s}^{-2}\)
Then:
| 1. | \(P_1=P_2=P_3\) | 2. | \(P_1<P_2<P_3\) |
| 3. | \(P_1=P_2\neq P_3\) | 4. | \(P_2=P_3\neq P_1\) |
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. | \(1333~\text{kg/m}^{3}\) |
Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are \(1.0~\text {cm}\) and \(3.0~\text{cm}\) respectively. Force exerted on the larger piston when a force of \(10~\text N\) is applied to the smaller piston:
1. \(80~\text N\)
2. \(90~\text N\)
3. \(10~\text N\)
4. \(20~\text N\)
| 1. | \(9.8\times 10^4\) Pa | 2. | \(9.8\times 10^7\) Pa |
| 3. | \(3.9\times 10^5\) Pa | 4. | \(4.9\times 10^6\) Pa |
A hydraulic press can lift \(100\) kg when a mass \(m\) is placed on the smaller piston. If the diameter of the larger piston is increased by a factor of \(4\) and the diameter of the smaller piston is reduced by a factor of \(4,\) while keeping the same mass \(m\) on the smaller piston, the press can lift:
1. \(2500 ~\text{kg}\)
2. \(50000 ~\text{kg}\)
3. \(25600 ~\text{kg}\)
4. \(550000 ~\text{kg}\)
Pressure on a swimmer \(10\) m below the surface of a lake is:
(Atmospheric pressure= \(1.01\times10^{5}\) Pa, density of water = \(1000\) kg/m3 and \(g=10\) m/s2)
1. \(5\) atm
2. \(4\) atm
3. \(2\) atm
4. \(3\) atm
In the figure shown, if the tank \((\mathrm a)\) has a circular cross-section and the tank \((\mathrm b)\) has a square cross-section, then when filled with water, we can conclude that:
| 1. | The pressure at the bottom of \((\mathrm a)\) is greater than that at the bottom of \((\mathrm b).\) |
| 2. | The pressure at the bottom of \((\mathrm a)\) is smaller than that at the bottom of \((\mathrm b).\) |
| 3. | The pressure at the bottom of \((\mathrm a)\) and \((\mathrm b)\) are the same. |
| 4. | The pressure at the bottom of the tank depends on the shape of the container. |
| 1. |  |
2. |  |
| 3. |  |
4. |  |
During a blood transfusion, the needle is inserted in a vein where the gauge pressure is \(2000~\text{Pa}.\) At what height must the blood container be placed so that blood may just enter the vein?
(the density of whole blood is \(1.06\times10^{3}~\text{kg/m}^3\))
1. \(0.163~\text m\)
2. \(0.192~\text m\)
3. \(0.157~\text m\)
4. \(0.754~\text m\)
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