MHT CET · Physics · Mechanical Properties of Solids
The density and bulk modulus of a metal bar is ' \(\mathrm{e}\) ' and ' \(\mathrm{K}\) ' respectively. When pressure 'P' is applied from all sides to that metal bar, the increase in its density is
- A \(\frac{Q P}{(K+P)}\)
- B \(\frac{Q P}{(K-P)}\)
- C \(\frac{K-P}{Q}\)
- D \(\frac{\mathrm{K}+\mathrm{P}}{\mathrm{Q}}\)
Answer & Solution
Correct Answer
(B) \(\frac{Q P}{(K-P)}\)
Step-by-step Solution
Detailed explanation
\(\rho=\mathrm{M} / \mathrm{V}\)
\(\frac{\mathrm{d} \rho}{\rho}=-\frac{\mathrm{dV}}{\mathrm{V}}\)
\(\mathrm{k}=-\frac{\mathrm{P}}{\mathrm{dV}}{\mathrm{V}}\)
\(-\frac{\mathrm{dV}}{\mathrm{V}}=\frac{\mathrm{P}}{\mathrm{k}}\)
\(\frac{\mathrm{d} \rho}{\rho}=\frac{\mathrm{P}}{\mathrm{k}}\)
\(\Rightarrow \mathrm{d} \rho=\frac{\rho \mathrm{P}}{\mathrm{k}}\)
\(\frac{\mathrm{d} \rho}{\rho}=-\frac{\mathrm{dV}}{\mathrm{V}}\)
\(\mathrm{k}=-\frac{\mathrm{P}}{\mathrm{dV}}{\mathrm{V}}\)
\(-\frac{\mathrm{dV}}{\mathrm{V}}=\frac{\mathrm{P}}{\mathrm{k}}\)
\(\frac{\mathrm{d} \rho}{\rho}=\frac{\mathrm{P}}{\mathrm{k}}\)
\(\Rightarrow \mathrm{d} \rho=\frac{\rho \mathrm{P}}{\mathrm{k}}\)
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