Multiple choice

The pendulum of a clock is made of brass. If the clock keeps correct time at $20^{\circ}C$ .Calculate how many seconds per day will it loose at $35^{\circ}C$ $(\alpha $ for brass =$2 \times$$10^{-5} $$^oC$)

  1. 12.96 s

  2. 1.29 s

  3. 129.6 s

  4. 8.64 s
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A Correct answer
Explanation

The time period of a pendulum is T = 2 * pi * sqrt(L/g). The change in time is given by delta T = (1/2) * alpha * delta theta * T. For one day (86400 seconds), the loss is (1/2) * (2 * 10^-5) * (35 - 20) * 86400 = 10^-5 * 15 * 86400 = 12.96 seconds.

AI explanation

To find the time lost by the brass pendulum clock, apply the formula for fractional change in time, which is half the product of the coefficient of linear expansion and the temperature change. The calculation is 0.5 multiplied by 2 multiplied by 10^(-5) and multiplied by 15, yielding a fractional loss of 1.5 multiplied by 10^(-4). We then multiply this fraction by the total number of seconds in a day, 86400, to get 12.96 seconds. The clock will lose 12.96 seconds per day.

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