Question

As the temperature is increased, the time period of a pendulum

• A. increases as its effective length increases even though its centre of mass still remains at the centre of the bob
• B. decreases as its effective length increases even though its centre of mass still remains at the centre of the bob
• C. increases as its effective length increases due to shifting of centre of mass below the centre of the bob
• D. decreases as its effective length remains same but the centre of mass shifts above the centre of the bob

Answer 1

Answer: (A)

Time period of the simple pendulum is
$T=2\pi \sqrt{\frac{L}{g}}\dots \left(i\right)$
where $L$ is the effective length of the pendulum. With increase in temperature, the effective length $\left(L\right)$ of simple pendulum increases even though its centre of mass still remains at the centre of the bob.
From $\left(i\right)$, $T\propto \sqrt{L}$
So $T$ increases as temperature increases.