Question

The bulk modulus of a liquid is 3 × 10¹⁰ Nm^-2. The pressure required to reduce the volume of liquid by 2% is

• A. 3 × 10⁸ Nm^–2
• B. 9 × 10⁸ Nm^–2
• C. 6 × 10⁸ Nm^–2
• D. 12 × 10⁸ Nm^–2

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the pressure required to reduce the volume of a liquid by 2% given that the bulk modulus of the liquid is 3 × 10¹⁰ Nm^-2.

The bulk modulus (K) is defined as:

K = -\frac{\Delta P}{\frac{\Delta V}{V}}

Here, \Delta P is the change in pressure, \Delta V is the change in volume, and V is the original volume.

Rearranging the formula to solve for the change in pressure:

\Delta P = -K \times \frac{\Delta V}{V}

The problem states a 2% reduction in volume, which means:

\frac{\Delta V}{V} = \frac{2}{100} = 0.02

Substituting the given values into the formula:

\Delta P = -3 \times 10^{10} \, \text{Nm}^{-2} \times (-0.02)

Note: The negative sign in the formula reflects that the volume decreases due to an increase in pressure.

Calculating the pressure:

\Delta P = 3 \times 10^{10} \, \text{Nm}^{-2} \times 0.02 = 6 \times 10^{8} \, \text{Nm}^{-2}

Therefore, the pressure required to reduce the volume by 2% is 6 × 10⁸ Nm^-2.