Question

If the length of a second pendulum is increased $4$ %.What will be new time period ?

• A. $1.06sec$
• B. $1.02sec$
• C. $1.09sec$
• D. $1.55sec$

Answer 1

The correct option is B $1.02sec$

$\begin{array}{c}\text{Given- Length of the Second Pendulum increased by 4\%}\\ \text{we know That -}\\ T=2\pi \cdot \sqrt{\frac{l}{g}}-\text{(1)}\end{array}$

$\begin{array}{c}\text{By error analysis method}\\ \text{Taking logarithm in above eq-}\\ \log T=\frac{1}{2}\cdot \log \left(l\right)+\log \left(\frac{2\pi }{\sqrt{g}}\right)\end{array}$

$\begin{array}{c}\text{difterentiating Both sides}\\ \frac{dT}{T}=\frac{1}{2}\cdot \frac{dl}{l}=\frac{1}{2}\times 4\%=2\%=0.02\end{array}$

$\begin{array}{c}\text{Hence Time period of Pendulum}\\ T=1+0.02sec=1.02sec.\end{array}$