The pendulum of a block consists of a small heavy bob at the end of a brass rod.

Question

The pendulum of a block consists of a small heavy bob at the end of a brass rod. The clock keeps accurate time at 20 degrees Celsius at which the pendulum has a period of 0.5520 sec. By how much will it be in error after one day at 35 degrees Celsius?

Explanation / Answer

By T = 2p xv[L/g] =>As the L increases with temperature =>T will increase =>the clock will be slow By Lt = Lo[1+ a x ?t*C] =>Lt = Lo[1 + 19 x 10^-6 x (35-20)] =>Lt = 1.000285Lo Thus T20*C = 2p xv[Lo/g] --------------(i) & T35*C = 2p xv[Lt/g] ----------------(ii) =>By (ii)/(i) :- =>T35*C/T20*C = v[Lt/Lo] =>[T35*C/T20*C] = v1.000285 =>T35*C = 0.5520 x 1.0001424898 = 0.5520786544 sec Thus ?t/sec = 0.5520786544 - 0.5520 = 7.86544 x 10^-5 Thus ?t in 24 hour = 24 x 60 x 60 x 7.86544 x 10^-5 =>Thus ?t in 24 hour = 6.80 sec

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