Question

As the temperature is increased, the time period of a pendulum
(a) increases proportionately with temperature
(b) increases
(c) decreases
(d) remains constant

Answer 1

(b) increases
In general, the time period of a pendulum,t, is given by
$t=\frac{1}{2\pi }\sqrt{\frac{l}{g}}$.
When the temperature (T) is increased, the length of the pendulum (l) is given by,
$l=l_0(1+\alpha T)$,
where l₀ = length at 0 ^oC
$\alpha$= linear coefficient of expansion.
Therefore, the time period of a pendulum will be
$t=\frac{1}{2\pi }\sqrt{\frac{l_0(1+\alpha T)}{g}}$
Hence, time period of a pendulum will increase with increase in temperature.