Question

How much time a second pendulum gain or lose in a day if its length is increased by 2%?

• A. A gain of $3$%
• B. A loss of $1$%
• C. A gain of $2$%of total time in a day
• D. A loss of $2$%of total time in a day

Answer 1

The correct option is B A loss of $1$%

$\text{Given- * length increased by}2\%\text{of the pendulum.}$

$\begin{array}{c}\text{we know the formula}\\ T=2\pi \cdot \sqrt{\frac{l}{g}}\end{array}$

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

$\begin{array}{c}\text{Differentiating both sides-}\\ \frac{dT}{T}=\frac{1}{2}\cdot \frac{dl}{l}=\frac{1}{2}\times 2\%=1\%\end{array}$

$\begin{array}{c}\text{- The time beriod increases by}1\%\\ \text{and Hence the day will lose}1\%\text{of the time.}\end{array}$