question_answer

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T = 0°C. If the temperature of the wire is increased and the corresponding charge in its time period is plotted against its temperature, the resulting graph is a line of slop S. If the coefficient of linear expansion of metal is a then the value of S is :   JEE Main Online Paper (Held On 09 April 2016)

A) \[\frac{1}{\alpha }\]                                                       

B) \[2\alpha \]                

C) \[\frac{\alpha }{2}\]                                                       

D) \[\alpha \]                

Correct Answer: D

Solution :

                \[{{t}_{0}}=2=2\pi \sqrt{\frac{{{\ell }_{0}}}{g}}\] \[t=2\pi \sqrt{\frac{{{\ell }_{0}}(1+\alpha T)}{g}}=2{{(1+\alpha T)}^{1/2}}=2+\alpha T\] \[t-{{t}_{0}}=\alpha T\Rightarrow \Delta t=\alpha T\]