If the length of a simple pendulum is decreased by $4 \%$, then the time period

Question

Professor PC Thomas Classes · Answer

(a) : Time period $T = 2\pi\sqrt{\frac{l}{g}}$. This implies $T \propto l^{1/2}$. For small percentage changes, we can use approximation: $\frac{\Delta T}{T} 	imes 100 = \frac{1}{2} \left(\frac{\Delta l}{l} 	imes 100ight)$. Given that length is decreased by $4\%$, so $\frac{\Delta l}{l} 	imes 100 = -4\%$. Therefore, $\frac{\Delta T}{T} 	imes 100 = \frac{1}{2}(-4\%) = -2\%$. The negative sign indicates a decrease, so the time period decreases by $2\%$.