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Question
As the temperature is increased, the time period of a pendulum
Options
increases proportionately with temperature
increases
decreases
remains constant
Solution
increases
In general, the time period of a pendulum,t, is given by
t = `1/(2pi) sqrt(1/g)`
When the temperature (T) is increased, the length of the pendulum (l) is given by,
l =l0(1+∝T),
where l0 = length at 0 oC
∝ = linear coefficient of expansion.
Therefore, the time period of a pendulum will be
t = `1/(2pi) sqrt ((l_0(1+∝T))/g)`
Hence, time period of a pendulum will increase with increase in temperature.
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