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)

1.01 T

Answer 2

$T \propto l^{1 / 2}$ $\Rightarrow \frac{\Delta T}{T} =\frac{1}{2}\left(\frac{\Delta l}{l}\right)$ $\frac{\Delta T}{T} =\frac{1}{2}(2 \%)=1 \%$ $\Rightarrow \frac{T'-T}{T} =\frac{1}{100}$ $\Rightarrow T'=T+0.01 \,T$ $\Rightarrow T' =1.01 \, T$