Question

The length of a simple pendulum is increased by $44\%$. Then percentage increase in its time period will be

• A. $44\%$
• B. $22\%$
• C. $20\%$
• D. $11\%$

Answer 1

The correct option is C $20\%$

$\text{Given- length of Simple pendulum increased by}44\%$

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

$\begin{array}{c}\text{Sinu there is a change more than}4\%\text{in the length}\\ \text{Then we will use normal analysis.}\end{array}$

$\begin{array}{c}\text{Let when length increased by}44\%\\ \Rightarrow \text{length}{\ell }^{\prime }=1.44\ell \\ \text{and Time period be}{T}^{\prime }\end{array}$

$\begin{array}{c}{T}^{\prime }=2\pi \sqrt{\frac{1.44l}{g}}=2\pi \sqrt{\frac{l}{g}}\times \left(1.2\right)\\ T^{\prime }=T\times \left(1.2\right)=1.2T\end{array}$

$\text{\% change}=\frac{T^{\prime }-T}{T}\times 100=\frac{0.2T}{T}\times 100=20\%$