Q. No.Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below.
| Statement I: | Pressure of fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid. |
| Statement-II: | Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension. |
| 1. | Statement I is true but Statement II is false. |
| 2. | Both Statement I and Statement II are false. |
| 3. | Both Statement I and Statement II are true. |
| 4. | Statement I is false but Statement II is true. |
Subtopic: Pressure |
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Level 2: 60%+
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A cylindrical tube \(AB\) of length \(l\), closed at both ends contains an ideal gas of \(1\) mol having molecular weight \(M\). The tube is rotated in a horizontal plane with constant angular velocity \(\omega\) about an axis perpendicular to \(AB\) and passing through the edge at end \(A\), as shown in the figure. If \(P_A\) and \(P_B\) are the pressures at \(A\) and \(B\) respectively, then (Consider the temperature is same at all points in the tube)
1. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2}{ 2 R T}\right)~\)
2. \(P_B=P_A~\)
3. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2 }{3 R T}\right) ~\)
4. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2 }{R T}\right)~\)
1. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2}{ 2 R T}\right)~\)
2. \(P_B=P_A~\)
3. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2 }{3 R T}\right) ~\)
4. \(P_B=P_A \exp \left(\dfrac{M \omega^2 l^2 }{R T}\right)~\)
Subtopic: Pressure |
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Two cylindrical vessels of equal cross sectional area of \(2 ~\text m^2\) contain water up to heights \(10 ~\text m\) and \(6 ~\text m,\) respectively. If the vessels are connected at their bottom then the work done by the force of gravity is: (Density of water is \(10^3 ~\text{kg/m}^3\) and \(g = 10 \text{ m/s}^2\) )
1. \(4\times 10^4~\text J\)
2. \(6\times 10^4~\text J\)
3. \(1\times 10^5~\text J\)
4. \(8\times 10^4~\text J\)
1. \(4\times 10^4~\text J\)
2. \(6\times 10^4~\text J\)
3. \(1\times 10^5~\text J\)
4. \(8\times 10^4~\text J\)
Subtopic: Pressure |
Level 4: Below 35%
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A vessel with square cross-section and height of \(6 ~\text m\) is vertically partitioned. A small window of \(100 \text{ cm}^2\) with hinged door is fitted at a depth of \(3 \text{ m}\) in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density \(1.5 \times 10^3 ~\text{kg/m}^3.\) What force one needs to apply on the hinged door so that it does not get opened? Acceleration due to gravity \(= 10 ~\text{m/s}^2\))
1. \(150~\text N\)
2. \(200~\text N\)
3. \(130~\text N\)
4. \(140~\text N\)
1. \(150~\text N\)
2. \(200~\text N\)
3. \(130~\text N\)
4. \(140~\text N\)
Subtopic: Pressure |
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In a hydraulic lift, the surface area of the input piston is \(6\) cm2 and that of the output piston is \(1500\) cm2. If \(100\) N force is applied to the input piston to raise the output piston by \(20\) cm, then the work done is: (in kJ)
1. \(5\)
2. \(10\)
3. \(50\)
4. \(100\)
1. \(5\)
2. \(10\)
3. \(50\)
4. \(100\)
Subtopic: Pressure |
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Level 2: 60%+
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Mercury is filled in a tube of radius \(30~\text{cm}.\)
1. \(198~\text N\)
2. \(136~\text N\)
3. \(177~\text N\)
4. \(154~\text N\)
1. \(198~\text N\)
2. \(136~\text N\)
3. \(177~\text N\)
4. \(154~\text N\)
Subtopic: Pressure |
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In a hydraulic lift, a force \(F\) is applied to balance a load of \(10~\text{N}.\) The diameter of the effort piston is \(14~\text{cm}\) and the diameter of the load piston is \(1.4~\text{cm}.\) The value of the applied force \(F\) is equal to:
1. \(500~\text{N}\)
2. \(100~\text{N}\)
3. \(2000~\text{N}\)
4. \(1000~\text{N}\)
1. \(500~\text{N}\)
2. \(100~\text{N}\)
3. \(2000~\text{N}\)
4. \(1000~\text{N}\)
Subtopic: Pressure |
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An air bubble having volume \(1\) cm3 at depth 40 m inside water comes to surface. What will be the volume of the bubble at the surface?
1. \(5 ~cm^3\)
2. \(2 ~cm^3\)
3. \(4 ~cm^3\)
4. \(3 ~cm^3\)
1. \(5 ~cm^3\)
2. \(2 ~cm^3\)
3. \(4 ~cm^3\)
4. \(3 ~cm^3\)
Subtopic: Pressure |
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A light cylindrical vessel is kept on a horizontal surface. The area of the base is \(A.\) A hole of cross-sectional area \('a’\) is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid (\(a << A\)) is:
1. none of these
2. \(\dfrac{2a}{A}\)
3. \(\dfrac{A}{2a}\)
4. \(\dfrac{a}{A}\)
1. none of these
2. \(\dfrac{2a}{A}\)
3. \(\dfrac{A}{2a}\)
4. \(\dfrac{a}{A}\)
Subtopic: Pressure |
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Level 2: 60%+
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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. \(550000 ~\text{kg}\)
Subtopic: Pressure |
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Level 2: 60%+
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