question_answer

A pendulum clock loses 12s a day if the temperature is 40°C and gains 4s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the coefficient of linear expansion of the metal of the pendulum shaft are respectively:-                                                                                                [JEE MAIN - I 3-4-2016]

A) \[{{55}^{o}}C;\alpha =1.85\times {{10}^{-2}}{{/}^{o}}C\]

B) \[{{25}^{o}}C;\alpha =1.85\times {{10}^{-5}}{{/}^{o}}C\]

C) \[{{60}^{o}}C;\alpha =1.85\times {{10}^{-4}}{{/}^{o}}C\]

D) \[{{30}^{o}}C;\alpha =1.85\times {{10}^{-3}}{{/}^{o}}C\]

Correct Answer: B

Solution :

[b]

When clock gain 12 sec

...(1)

When clock lose 4 sec.

...(2)

From equation (1) & (2)

from equation (1)