Question

The length of a simple pendulum is decreased by $21\%.$ The percentage change in its time period is :

• A. $11\%$ decrease
• B. $51\%$ increase
• C. $21\%$ decrease
• D. $31\%$ decrease

Answer 1

The correct option is A $11\%$ decrease

Time period of simple pendulum $T\propto \sqrt{l}$

where $l$ is the length of string.

$⟹$ $\frac{T^{\prime }}{T}=\sqrt{\frac{l^{\prime }}{l}}$

Final length of simple pendulum $L^{\prime }=l-0.21l=0.79l$
$\therefore$ $\frac{T^{{}^{\prime }}}{T}=\sqrt{\frac{l^{{}^{\prime }}}{l}}=\sqrt{\frac{.79l}{l}}=0.89$
$\therefore$ Thus new time period of simple pendulum $T^{{}^{\prime }}=0.89T$
Hence percentage decrease in time period $\Delta T=\frac{T-T^{\prime }}{T}\times 100$

$\therefore$ $\Delta T=\frac{T-0.89T}{T}\times 100=11$%