Question

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

• A. $10\%$
• B. $20\%$
• C. $40\%$
• D. $44\%$

Answer 1

The correct option is B $20\%$

T = $2\pi \sqrt{\frac{l}{g}}$
If the length or the pendulum is increased by $44\%$, the new length ​ $l^{\prime }=l+0.44l=1.44l$
Therefore, the new time period is $T^{\prime }=2\pi \sqrt{\frac{l^{\prime }}{g}}$
Thus$\frac{T^{\prime }}{T}=\sqrt{\frac{l^{\prime }}{l}}=\sqrt{\frac{1.44l}{l}}=\sqrt{1.44}=1.2or{T}^{\prime }=1.2T,$
i.e., the time period increases by 0.2T or the percentage increase is $\frac{0.2T}{T}\times 100=20\%$
Hence the correct choice is (b)