Question:
When the temperature of a metal wire is increased from \(0^{\circ}\mathrm{C}\) to \(10^{\circ}\mathrm{C}\), its length increases by \(0.02\%\). The percentage change in its mass density will be closest to :
When the temperature of a metal wire is increased from \(0^{\circ}\mathrm{C}\) to \(10^{\circ}\mathrm{C}\), its length increases by \(0.02\%\). The percentage change in its mass density will be closest to :
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Density \(\propto\) 1/volume and volume \(\propto l^3\) for isotropic expansion, so the density falls by about three times the fractional length change.
Updated On: Nov 5, 2026
- \(0.008\)
- \(0.06\)
- \(0.8\)
- \(2.3\)
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The Correct Option is B
Solution and Explanation
Mass is constant, so \(\rho=\frac{m}{V}\) and \(V\propto l^3\Rightarrow\rho\propto l^{-3}\).
\(\frac{\Delta\rho}{\rho}\approx-3\frac{\Delta l}{l}=-3\times0.02\%=-0.06\%\).
The density decreases by about \(0.06\%\).
Answer: (2) 0.06
\(\frac{\Delta\rho}{\rho}\approx-3\frac{\Delta l}{l}=-3\times0.02\%=-0.06\%\).
The density decreases by about \(0.06\%\).
Answer: (2) 0.06
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