Question 11 of 13beginner🔧 ApplyNumerical3 marks

Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.

Correct Answer

The fractional change in volume of the glass slab is 2.7×102.7 \times 10⁻⁵.

Exercise: EXERCISES | Q: 8.14
For More Understanding

Explanation

This numerical problem requires applying the definition of bulk modulus. The fractional change in volume (volume strain) is the ratio of hydraulic pressure to bulk modulus. The context provides the formula ΔV/V = stress/B and the conversion 1 atm = 1.013×101.013 \times 10⁵ Pa. The bulk modulus of glass (B = 37×1037 \times 10⁹ Nm⁻²) is a standard value from NCERT Table 8.3 (Bulk moduli of common materials), which would accompany Table 8.2 shown in the context.

Solution Steps

  1. Step 1: Convert pressure to SI units. P = 10 atm = 10×1.01310 \times 1.013 × 10⁵ Pa = 1.013×101.013 \times 10⁶ Pa

  2. Step 2: Identify the bulk modulus of glass. From standard NCERT data: B = 37×1037 \times 10⁹ Nm⁻²

  3. Step 3: Apply the formula for fractional change in volume. ΔV/V = P/B = (1.013×101.013 \times 10⁶)/(37×1037 \times 10⁹)

  4. Step 4: Calculate the result. ΔV/V = 1.013/(37×1037 \times 10³) = 1.013/37000 = 2.74×102.74 \times 10⁻⁵ ≈\approx 2.7×102.7 \times 10⁻⁵

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