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Does the time period of pendulum just increases with temperature or proportionately with temperature. If former is correct why latter is incorrect

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    $\begingroup$ As the length of string increases $\endgroup$ Mar 13 '19 at 1:30
  • $\begingroup$ I've edited your title. Please use titles that describe the question. $\endgroup$
    – user4552
    Mar 13 '19 at 4:31
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The period $T$ for a pendulum is given by the following equation.

$$T\approx 2\pi \sqrt{\frac Lg}$$

As you can see in this equation, the period depends only on the length $L$ of the pendulum and the acceleration $g$ of gravity. The pendulum's period increases proportionally to the square root of its length and the square root of gravitational acceleration. The effects of temperature on a pendulum are insignificant. Therefore the period of a pendulum does not increase proportionally with temperature.

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  • $\begingroup$ As a practical matter pendulum clocks need some kind of temperature compensation mechanism exactly because of the relation you cite. After all, the length of a naive pendulum depends on the temperature. There are two common schemes for building temperature compensated pendulums. $\endgroup$ Mar 14 '19 at 0:29
  • $\begingroup$ The OP's issue here may be one of understanding why a multiple choice question was marked as it was. If so the answer would be that the period is varies in proportion to the square root of temperature and not proportionally to the temperature. $\endgroup$ Mar 14 '19 at 0:30

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