MHT CET · Physics · Thermal Properties of Matter
A metal rod having coefficient of linear expansion \(2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\) is 0.75 m long at \(45^{\circ} \mathrm{C}\). When the temperature rises to \(65^{\circ} \mathrm{C}\), the increase in length of the rod will be
- A 3.0 mm
- B 0.75 mm
- C 0.30 mm
- D 0.15 mm
Answer & Solution
Correct Answer
(C) 0.30 mm
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \alpha & =\frac{\mathrm{d} l}{l \times \mathrm{dt}} \\ \mathrm{d} l & =\alpha \times l \times \mathrm{dt} \\ & =2 \times 10^{-5} \times 0.75 \times\left(65^{\circ}-45^{\circ}\right) \\ & =0.3 \times 10^{-3} \mathrm{~m}=0.30 \mathrm{~mm}\end{aligned}\)
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