Question

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

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

Answer 1

The correct option is D $20\%$

As we know,
The time period of simple pendulum,
$T=2\pi \sqrt{\frac{L}{g}}$
If it's length is increased by $44\%$
$T^{\prime }=2\pi \sqrt{\frac{L(1+44/100)}{g}}=(1\cdot 2)2\pi \sqrt{\frac{L}{g}}$
$\frac{T^{\prime }}{T}-1=0\cdot 2$
$(\frac{T^{\prime }}{T}-1)\times 100=20\%$
Final answer : (c)