Question

11.) If length of a simple pendulum is increased by 69%, then the percentage increase in its time period is
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Answer 1

$= 30\%$

Explanation:

$\frac{t_1}{t_2} = \sqrt (\frac {l_1}{l_2})$

$= \sqrt (\frac{l_1}{l_1+ 69 \%}) = \sqrt (\frac{l_1}{l_1+ 0.69l_1})$

$=\sqrt(\frac {l_1}{1.69l_1}) = \frac{1}{1.3}$

$t_2=1.3t1$

$t_2-t_1=1.3t_1-t_1$

$=0.3t_1$

$\frac{t_2-t_1}{t_1}=0.3$

$= 30\%$

Thus percentage increase in its time period is $= 30\%$

Answer 2

The percentage increase in its time period=30%

Explanation:

Let initial length of pendulum=l

Initial time period, $T_1=2\pi\sqrt{\frac{l}{g}}$

Length of pendulum increased by 69%

Then, length of pendulum=$l+\frac{69}{100}l=\frac{169}{100}l$

After increasing length of pendulum 69%,

Then,time period, $T_2=2\pi\sqrt{\frac{169l}{100g}$

$\frac{T_1}{T_2}=\frac{2\pi\sqrt{\frac{l}{g}}}{2\pi\sqrt{\frac{169l}{100g}}}}=\frac{10}{13}$

$\frac{T_2}{T_1}=\frac{13}{10}=1.3$

$T_2=1.3T_1$

Increase value in time period =$T_2-T_1=1.3T_1-T_1=0.3T_1$

Percentage increase in its time period=$\frac{Increase\;value}{initial\;value}\times 100$

Percentage increase in its time period=$\frac{0.3T_1}{T_1}\times 100=30$%

Hence, the percentage increase in its time period=30%

#Learns more:

https://brainly.in/question/3649229: Answered by brainly teacher