A block of wood is immersed in water (assume that the wood is impervious to water), and it floats half immersed. It is placed in an elevator which is accelerating upward. Then,

1. the block floats, slightly more of it out of the water.
2. the block floats, slightly less of it out of the water.
3. the block floats, half-immersed.
4. the block sinks completely.
Subtopic:  Archimedes' Principle |
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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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A cube floats both in water and in a liquid of specific gravity of \(0.8\). Therefore,

a. the apparent weight of the cube is the same in water and in liquid.
b. the cube has displaced an equal volume of water and liquid while floating.
c. the cube has displaced an equal weight of water and liquid while floating.
d. if some weights are placed on the top surface of the cube to make it just sink, the load in case of water will be \(0.8\) times of that to be used in case of liquid.
 
1. (a) and (c) both are correct.
2. only (d) is correct.
3. (a) and (b) both are correct.
4. (a), (b), and (c) are correct.
Subtopic:  Archimedes' Principle |
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The loss in weight of a lead block is \(3\) times in liquid \(A\) compared to that in liquid \(B\). In both cases, the block is half immersed. If \(\rho_A, \rho_B\) be the densities of the liquids and \(\rho_L\) the density of lead, then:

1. \(3\rho_A=\rho_B\)
2. \(\dfrac32\rho_A=\rho_B\)
3. \(\rho_A=\dfrac32\rho_B\)
4. \(\rho_A=3\rho_B\)
Subtopic:  Archimedes' Principle |
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A body floats in a liquid with \(40\%\) of its volume outside (exposed to air). If it is immersed in a liquid with double the density, then, the fraction exposed will be:
1. \(20\%\)
2. \(80\%\)
3. \(30\%\)
4. \(70\%\)
Subtopic:  Archimedes' Principle |
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