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प्रश्न
Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 109 N m−2.
उत्तर
Given:
Bulk modulus of water (B) = \[2 . 1 \times {10}^9 {\text{ Nm }}^{- 2}\]
In order to decrease the volume (V) of a water sample by 0.01%, let the increase in pressure be P.
\[\frac{V \times 0 . 01}{100} = ∆ V\]
\[ \Rightarrow \frac{∆ V}{V} = {10}^{- 4} \]
\[\text{ From B }= \frac{PV}{∆ V}, \text{ we have }: \]
\[ \Rightarrow P = B\left( \frac{∆ V}{V} \right)\]
\[ = 2 . 1 \times {10}^9 \times {10}^{- 4} \]
\[ = 2 . 1 \times {10}^5 \text{ N/ m}^2\]
Hence, the required increase in pressure is \[2 . 1 \times {10}^5 {\text{ Nm}}^{- 2}\] .
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