JEE Main 2016 · 9 Apr · Shift 1 · Physics Q25

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PhysicsSingle correct+4 / -1Question 25 of 90

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T = 0°C. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :

\dfrac\alpha2

2α

\dfrac1\alpha

Answer and worked solution

Official answer: A

$T=2\pi\sqrt{\frac{L_0(1+\alpha\theta)}g}\approx T_0\left(1+\frac{\alpha\theta}2\right)$ , so the slope is $S=\frac{T_0\alpha}2=\alpha$ for $T_0=2$ s.

Topics:Temperature and thermal expansion Simple and compound pendulum

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JEE Main 2016 · 9 Apr · Shift 1, Physics question 25