JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
A simple pendulum made of a bob of mass \(m\) and a metallic wire of negligible mass has time period \(2s\) at \(T = 0\,^oC\) . If the temeprature of the wire is increased and the corresponding change in its time peirod is plotted against its temperature, the resulting graph is a line of slope \(S\). If the coefficient of linear expansion of metal is \(\alpha \) then the value of \(S\) is
- A \(\frac {\alpha }{2}\)
- B \(2\alpha \)
- C \(\alpha \)
- D \(\frac {1}{\alpha }\)
Answer & Solution
Correct Answer
(C) \(\alpha \)
Step-by-step Solution
Detailed explanation
If coefficient of liner expansion is \(\alpha \) then \(\Delta T = \frac{1}{2}T\,\alpha \,d\,\theta \) \( \Rightarrow \frac{{\Delta T}}{{d\theta }} = \frac{T}{2}\alpha \) \(But\,T = 2s\) \(\therefore \,Line\,of\,slope\,S = \frac{{\Delta T}}{{d\theta }} = \alpha .\)
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