A clock which keeps correct time at 25 ° C , has a pendulum made of brass. The coefficient of linear expansion for brass is 0.000019 ° C - 1 . How many seconds a day will it gain if the ambient temperature falls to 0 ° C ?

Question

A clock which keeps correct time at 25 ° C , has a pendulum made of brass. The coefficient of linear expansion for brass is 0.000019 ° C - 1 . How many seconds a day will it gain if the ambient temperature falls to 0 ° C ?, 20.52 s, 15.00 s, 52.10 s, 63.10 s

MARKS App · Accepted Answer

Let L 0 and L 25 be the length of pendulum at 0 ° C and 25 ° C respectively. We know that, L 25 = L 0 1 + αT = L 0 1 + 0.000019 × 25 = 1.000475 L 0 ⇒ ΔL = L 25 − L 0 = 0 .000475 L 0 Also , T = 2 π L g From method of errors ⇒ ΔT T = 1 2 ΔL L here , ΔT = gain in time T = Total time of day = 24 × 60 × 60 sec ⇒ ΔT = 1 2 × 0.000475 L 0 L 0 × 24 × 60 × 60 sec ⇒ ΔT = 20 .52 sec

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