Question

Will a pendulum clock accurate at room temperature of 30⁰C gain or lose time when the temperature increases at 40⁰C?

Answer 1

As $T=2\pi\sqrt{\frac{l}{g}}$

This is the time taken by the pendulum for one oscillation.

If temperature increases by $10°C$ , then new length of pendulum $l'=l(1+\alpha∆T)$

Length of the pendulum increases so

$T'=2\pi\sqrt{\frac{l'}{g}}$

As $l'>l\implies T'>T$

So the pendulum takes more time for one oscillation. Hence, the clock loses time.