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

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decreases as its effective length increases even though its centre of mass still remains at the
centre of the bob.

increases as its effective length increases even though its centre of mass still remains at the
centre of the bob.

decreases as its effective length remains same but the centre of mass shifts above the centre
of the bob.

increases as its effective length increases due to shifting of centre of mass below the centre
of the bob

answer is A.

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Detailed Solution

Time period of the simple pendulum is

$T = 2 π \sqrt{\frac{L}{g}} . . . (i)$

where $L$ is the effective length of the pendulum. With increase in temperature, the effective length $(L)$ of simple pendulum increases even though its centre of mass still remains at the centre of the bob.

From (i), $T \propto \sqrt{L}$

So $T$ increases as temperature increases.

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