Two small drops of mercury, each of radius R, coalesce to form a

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 Multiple Choice QuestionsMultiple Choice Questions

141.

A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity  ω when

  • water levels in both sections A and B go up

  • water level in section A goes up and that in B comes down

  • water level in section A comes down and that in B it goes up

  • water levels remain same in both sections


142.

Assertion:  Specific gravity of a fluid is a dimensionless quantity

Reason: : It is the ratio of density of fluid to the density of water.

  • If both assertion and reason are true and reason is the correct explanation of assertion 

  • If both assertion and reason are true but reason is not the correct explanation of assertion

  • If assertion is true but reason is false

  • If both assertion and reason are false


143.

Assertion: For Reynold number Re > 2000, the flow of fluid is turbulent. 

Reason: Inertial forces are dominant compared to the
viscous forces at such high Reynold numbers.

  • If both assertion and reason are true and reason is the correct explanation of assertion

  • If both assertion and reason are true but reason is not the correct explanation of assertion

  • If assertion is true but reason is false

  • If both assertion and reason are false


144.

A sphere of mass Mand radius R is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

  • R2

  • R

  • 1/R

  • 1/R2


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145.

The old age arteries carrying blood in the human body become barrow resulting in an increase in blood pressure. This follows from

  • Pascal's law

  • Stoke's law

  • Bernoulli's principle

  • Archimedes principle


146.

Assertion: Smaller drops of liquid resist deforming forces better than the larger drops. 

Reason: Excess pressure inside a drop is directly proportional to its surface area

  • If both assertion and reason are true and reason is the correct explanation of assertion

  • If both assertion and reason are true but reason is not the correct explanation of assertion

  • If assertion is true but reason is false

  • If assertion is true but reason is false


147.

Bernoulli's equation is a consequence of conservation of

  • energy

  • linear momentum

  • angular momentum

  • mass


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148.

Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies  before and after  change is

  • 1 : 21/3

  • 21/3 : 1

  • 2 : 1

  • 1 : 2


B.

21/3 : 1

Radius of one drop of mercury is R

∴  The volume of one drop = 43π R3

∴  Total volume of the two drops,

  V =  2 × 43π R3

   V = 83 πR3

Let the radius of the large drop formed be R'

The total volume of the large is also V

    43π R'2 = 83π R3

     R'3 = 2R3

⇒   R' = 21/3 R

Now the surface area of the resultant drop is 

   S1 = 2 × 4πR2

   S1 = 8πR

and the surface area of the resultant drop is 

    S2 = 4πR'

    S2 = 4π 22/3 R2

Let T be the surface tension of the mercury. Therefore the surface energy of the two drops before coalescing is

     U1 = S1 T

     U1 = 8πR2T

and the surface energy after coalescing,

    U2 = S2

     U2 = 22/3 × 4πR2T

∴   U1U2 = 8π R2T223 × 4π R2T

           = 2223

    U1U2 = 21/3


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149.

Scent sprayer is based on

  • Charle's law

  • Archimedes principle

  • Boyle's law

  • Bernoulli's theorem


150.

The property utilized in the manufacture of lead shots is

  • specific weight of liquid lead

  • compressibility of liquid lead

  • specific gravity of liquid lead

  • surface tension of liquid lead


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