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MCQEasyJEE 2025Streamline & Turbulent Flow, Critical Velocity

JEE Physics 2025 Question with Solution

Consider the following statements: Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid. As the temperature of liquid rises, the coefficient of viscosity increases. As the temperature of gas increases, the coefficient of viscosity increases. The onset of turbulence is determined by Reynolds number. In a steady flow, two streamlines never intersect. Choose the correct answer from the options given below:

  • A

    A, B, C Only

  • B

    C, D, E Only

  • C

    B, C, D Only

  • D

    A, D, E Only

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Five statements about surface tension, viscosity, Reynolds number, and streamlines are to be checked.

Find: The correct set of statements.

Check each statement one by one:

  1. Statement A: Surface tension is associated with the surface molecules, which have higher potential energy than molecules in the interior because they experience unbalanced cohesive forces. Therefore, the given statement is incorrect.

  2. Statement B: For liquids, as temperature increases, viscosity decreases. Hence the given statement is incorrect.

  3. Statement C: For gases, viscosity increases with temperature. Hence this statement is correct.

  4. Statement D: The onset of turbulence is determined by the Reynolds number. Hence this statement is correct.

  5. Statement E: In a steady flow, two streamlines never intersect, because intersection would imply two different velocities at the same point, which is impossible. Hence this statement is correct.

Therefore, the correct statements are C, D and E only.

The correct option is B.

Note: The solution marks option D, but the worked analysis and final boxed result clearly conclude C, D and E only, which corresponds to option B.

Statement-wise Analysis

Given: The question asks which statements among A to E are correct.

Find: The correct combination.

Statement A says surface tension arises due to extra energy of molecules at the interior as compared to molecules at the surface. This is wrong because the reverse is true: molecules at the surface possess extra energy.

Statement B says viscosity of a liquid increases with temperature. This is wrong because, for liquids, viscosity decreases as temperature rises.

Statement C is correct because gas viscosity increases with temperature due to enhanced molecular motion and momentum transfer.

Statement D is correct because Reynolds number determines whether flow remains laminar or becomes turbulent.

Statement E is correct because streamlines cannot intersect in steady flow.

So the true statements are C, D, E only.

Hence, the correct option is B.

Common mistakes

  • Assuming statement A is correct by confusing surface molecules with interior molecules. Surface tension arises because surface molecules have higher energy due to unbalanced cohesive forces. Always compare surface molecules with interior molecules in the correct direction.

  • Using the liquid-viscosity trend for gases as well. In liquids, viscosity decreases with temperature, but in gases it increases. Do not apply the same temperature dependence to both states of matter.

  • Trusting the displayed option label without checking the worked solution. Here, the page says option D, but the actual statement-wise analysis gives C, D, E only, which matches option B. Always map the final correct statement set back to the options.

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