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Q. No.A viscous liquid is flowing through a straight tube under the action of a pressure difference across the ends of the tube. The tube is aligned with the \(x\)-axis. The force exerted on the tube by the liquid has the form:
\((a,b>0)\)
\((a,b>0)\)
| 1. | \(a\hat i\) | 2. | \(-a\hat i\) |
| 3. | \(a\hat i+b\hat j\) | 4. | \(-a\hat i+b\hat j\) |
Subtopic: Viscosity |
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A spherical raindrop of mass \(m\) falls from the sky with a uniform velocity \(v,\) its weight being balanced by the viscous force of air resistance. The velocity \(v\) and the mass of the drop are related by:
1. \(v\propto m\)
2. \(v^3\propto m\)
3. \(v^3\propto m^2\)
4. \(v^2\propto m^3\)
1. \(v\propto m\)
2. \(v^3\propto m\)
3. \(v^3\propto m^2\)
4. \(v^2\propto m^3\)
Subtopic: Stokes' Law |
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A cubical block of wood of mass \(m\) floats in water, with \(\Large\frac23\) of the wood immersed underwater. The area of a face of the wooden block is \(A.\) The pressure of water acting on the lowest face is:
| 1. | \(\Large\frac{mg}{A}\) | 2. | \(\Large\frac{2}{3}\frac{mg}{A}\) |
| 3. | \(\Large\frac{1}{3}\frac{mg}{A}\) | 4. | \(\Large\frac{3}{2}\frac{mg}{A}\) |
Subtopic: Pressure |
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A wedge shaped vessel holds water. As one moves downward along \(OB\) or \(AB\) pressure changes. The increase in pressure per unit distance traversed,
| 1. | is more along \(AB\) compared to \(OB\) |
| 2. | is more along \(OB\) compared to \(AB\) |
| 3. | is the same along \(AB\) or \(OB\) |
| 4. | is zero along \(AB,\) but non-zero along \(OB\) |
Subtopic: Pressure |
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When two homogeneous bodies \(A,B\) are floated in water, they are found to be submerged differently. Both bodies have the same cross-section, and the exposed parts of both are of the same height \(L.\)Then:
| 1. | Weight of \(A=\dfrac{1}{3}\) weight of \(B\) |
| 2. | Weight of submerged part of \(A=\dfrac{1}{2}\) weight of submerged part of \(B\) |
| 3. | Density of \(A=\dfrac{3}{4}\) the density of \(B\) |
| 4. | Weight of exposed part of \(A=\) weight of exposed part of \(B\) |
Subtopic: Archimedes' Principle |
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Given below are two statements:
| Assertion (A): | The viscosity of a gas decreases as the temperature is increased. |
| Reason (R): | When temperature increases, the random molecular motion of the gas molecules increases. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Viscosity |
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The surface tension of soapy water is \(S.\) When bubbles are blown with soapy water, one bubble of radius \(r\) is formed within another of radius \(3r.\) The excess pressure within the smaller bubble, relative to the atmospheric pressure is:
| 1. | \(\dfrac{4S}{r}\) | 2. | \(\dfrac{8S}{3r}\) |
| 3. | \(\dfrac{8S}{r}\) | 4. | \(\dfrac{16S}{3r}\) |
Subtopic: Surface Tension |
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A vessel of water \((A)\) contains pure water while a second vessel of water \((B)\) is filled with sea water. If a toy-boat is floated in both the vessels, then:
| 1. | it will displace less weight of water in \(A\) than in \(B.\) |
| 2. | it will displace less volume of water in \(A\) than in \(B.\) |
| 3. | it will displace more weight of water in \(A\) than in \(B.\) |
| 4. | it will displace more volume of water in \(A\) than in \(B.\) |
Subtopic: Archimedes' Principle |
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Two identically wide and deep streams \(A,B\) merge together to form a stream \(C:\) the latter having the same depth but double the width of the former. The speeds of water in \(A\) and \(B\) are \(v_A,v_B\) while that in \(C\) is \(v_C.\) Then:
1. \(v_A+v_B=v_C\)
2. \(v_A+v_B=\dfrac{1}{2}v_C\)
3. \(v_A+v_B=2v_C\)
4. \(v_A+v_B=4v_C\)
1. \(v_A+v_B=v_C\)
2. \(v_A+v_B=\dfrac{1}{2}v_C\)
3. \(v_A+v_B=2v_C\)
4. \(v_A+v_B=4v_C\)
Subtopic: Equation of Continuity |
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A thin spherical shell of radius \(R,\) thickness \(t,\) made of a metal of density \(\large{\rho}_{\small{S}},\) floats half submerged in a vessel containing a liquid of density \(\large{\rho}_{\small{L}}.\) The ratio \(\dfrac{\large{\rho}_{\small{S}}}{\large{\rho}_{\small{L}}}\) is equal to:
| 1. | \(\dfrac{R}{6t}\) | 2. | \(\dfrac{R}{3t}\) |
| 3. | \(\dfrac{6t}{R}\) | 4. | \(\dfrac{3t}{R}\) |
Subtopic: Archimedes' Principle |
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