Question

Time period of a simple pendulum is $T$. If its length increases by $2\%$, the new time period becomes

• A. 0.98 T
• B. 1.02 T
• C. 0.99 T
• D. 1.01 T

Answer 1

Answer: (D)

$T\propto l^{1/2}$
$\Rightarrow \frac{\Delta T}{T}=\frac{1}{2}\left(\frac{\Delta l}{l}\right)$
$\frac{\Delta T}{T}=\frac{1}{2}(2\%)=1\%$
$\Rightarrow \frac{T;-T}{T}=\frac{1}{100}$
$\Rightarrow T^{\prime }=T+0.01T$
$\Rightarrow T^{\prime }=1.01T$