Fractional Change in Volume under Pressure Difference – Rankers Physics

Solids: Practice Problem & Solution

A metal block is experiencing an atmospheric pressure of \(1 \times 10^5\text{ N/m}^2\). When the same block is placed in a vacuum chamber, the fractional change in its volume is (the bulk modulus of metal is \(1.25 \times 10^{11}\text{ N/m}^2\))
\(4 \times 10^{-7}\)
\(2 \times 10^{-7}\)
\(8 \times 10^{-7}\)
\(1 \times 10^{-7}\)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

The bulk modulus is defined as \(B = \frac{\Delta P}{\Delta V/V}\). Moving to vacuum causes a pressure change of \(\Delta P = 10^5\text{ N/m}^2\). Thus, the fractional volume change is \(\frac{\Delta V}{V} = \frac{\Delta P}{B} = \frac{10^5}{1.25 \times 10^{11}} = 8 \times 10^{-7}\).

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