Question

A pendulum clock keeps correct time at 20oC. The coefficient of linear expansion of pendulum is . If the room temperature increases to 40oC, how many seconds will the clock lose or gain per day?

Solution

Correct option is

10.37 s

 

The time period of a pendulum clock is given by 

                      

                   …(i)

Partially differentiating we get

                    

Dividing (ii) by (i) we have

                    

Where α is the coefficient of linear expansion and ∆θ is the rise in temperature. Thus 

                    

Now, the time period of a pendulum clock T = 1s. Thus the clock gains 12 × 10–5 s every second. In a day (= 86400 s), the clock will gain 12 × 10–5× 86400 = 10.37 s.

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