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NEET PHYSICSMechanical Properties of FluidEasy

Question

A rectangular film of liquid is extended from (4 cm×2 cm)(4 \text{ cm} \times 2 \text{ cm}) to (5 cm×4 cm)(5 \text{ cm} \times 4 \text{ cm}). If the work done is 3×104 J3 \times 10^{-4} \text{ J}, then the value of the surface tension of the liquid is:

A

0.250 Nm10.250 \text{ Nm}^{-1}

B

0.125 Nm10.125 \text{ Nm}^{-1}

C

0.2 Nm10.2 \text{ Nm}^{-1}

D

8.0 Nm18.0 \text{ Nm}^{-1}

Step-by-Step Solution

  1. Surface Energy Relation: The work done (WW) to increase the surface area of a liquid film is equal to the increase in surface energy, which is given by the product of surface tension (TT) and the total change in surface area (ΔA\Delta A). The formula is W=T×ΔAW = T \times \Delta A .
  2. Area Calculation:
  • Initial Area, A1=4 cm×2 cm=8 cm2=8×104 m2A_1 = 4 \text{ cm} \times 2 \text{ cm} = 8 \text{ cm}^2 = 8 \times 10^{-4} \text{ m}^2.
  • Final Area, A2=5 cm×4 cm=20 cm2=20×104 m2A_2 = 5 \text{ cm} \times 4 \text{ cm} = 20 \text{ cm}^2 = 20 \times 10^{-4} \text{ m}^2.
  • Change in area (one side) = 208=12×104 m220 - 8 = 12 \times 10^{-4} \text{ m}^2.
  1. Accounting for Two Surfaces: A liquid film (like a soap film) has two free surfaces (top and bottom). Therefore, the total increase in effective surface area is twice the geometric increase: ΔAtotal=2×(A2A1)=2×12×104=24×104 m2\Delta A_{total} = 2 \times (A_2 - A_1) = 2 \times 12 \times 10^{-4} = 24 \times 10^{-4} \text{ m}^2
  2. Calculation: Substituting the values into the work formula: 3×104=T×(24×104)3 \times 10^{-4} = T \times (24 \times 10^{-4}) T=3×10424×104=324=18=0.125 Nm1T = \frac{3 \times 10^{-4}}{24 \times 10^{-4}} = \frac{3}{24} = \frac{1}{8} = 0.125 \text{ Nm}^{-1}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Mechanical Properties of Fluid. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMechanical Properties of Fluidrectangularliquidextendedsurfacetension

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