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MP DTE Mechanical Properties of Solids and Fluids — practice questions — page 2

Explore 35 free Mechanical Properties of Solids and Fluids questions in MP DTE Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Mechanical Properties of Solids and Fluids questions and exercises with answers

Showing questions 31–35 of 35.

Worked practice questions

For thin spherical shell of water (radius R, thickness t), volume of water:

  1. π R²
  2. V = 0
  3. (4/3)π R³
  4. ≈ 4π R² t (for t << R, approximate via differential)
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Correct answer: D. ≈ 4π R² t (for t << R, approximate via differential)

dV/dR = 4πR² (surface area). Thin shell V ≈ 4πR² × t for t << R. Useful in fluid dynamics, atomic structure (shell-by-shell electron density).

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For dynamic surface tension in oil drop slowly forming at tip of pipette, drop falls when:

  1. Drop weight = 1
  2. Drop weight ≥ surface tension force (= γ × circumference)
  3. Random
  4. Always falls
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Correct answer: B. Drop weight ≥ surface tension force (= γ × circumference)

Drop hangs by surface tension force γ × 2πr until weight exceeds it: mg = γ × 2πr → drop falls. Used in stalagmometer to measure surface tension by counting drops/volume.

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Compressibility (1/B) of water at standard conditions:

  1. 10⁻¹⁸
  2. 1 Pa⁻¹
  3. Cannot determine
  4. About 4.6 × 10⁻¹⁰ Pa⁻¹ (B ≈ 2.2 × 10⁹ Pa)
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Correct answer: D. About 4.6 × 10⁻¹⁰ Pa⁻¹ (B ≈ 2.2 × 10⁹ Pa)

Water bulk modulus B ≈ 2.2 GPa. Compressibility = 1/B ≈ 4.6 × 10⁻¹⁰ Pa⁻¹. Means 1 atm causes ~5 × 10⁻⁵ volume change. Water is nearly incompressible — hence assumption valid in hydraulics.

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