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

Solution

## The correct option is B $$1.02sec$$$$\begin{array}{l} \text { Given- Length of the Second Pendulum increased by 4% } \\ \text { we know That - } \\ \qquad T=2 \pi \cdot \sqrt{\frac{l}{g}}-\text { (1) } \end{array}$$ $$\begin{array}{l} \text { By error analysis method } \\ \text { Taking logarithm in above eq- } \\ \qquad \log T=\frac{1}{2} \cdot \log (l)+\log \left(\frac{2 \pi}{\sqrt{g}}\right) \end{array}$$ $$\begin{array}{l} \text { difterentiating Both sides } \\ \qquad \frac{d T}{T}=\frac{1}{2} \cdot \frac{d l}{l}=\frac{1}{2} \times 4 \%=2 \%=0.02 \end{array}$$ $$\begin{array}{l} \text { Hence Time period of Pendulum } \\ \qquad T=1+0.02 \mathrm{sec}=1.02 \mathrm{sec} . \end{array}$$Physics

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