Question

Calculate the change in time period if its length increases by 125%. ​

Answer 1

$t = 2\pi \sqrt{ \frac{l}{g} }$

now,

length increases by 125%

$l 1= l + \frac{125 \: l}{100} \\ l \: 1 = \frac{225 \: l}{100}$

$t \: 1 = 2\pi \sqrt{ \frac{225 \: l}{100 \: g} }$

$\frac{t}{t1} = \sqrt{ \frac{l}{g} \times \frac{100g}{225l} }$

$\frac{t}{t1} = \sqrt{ \frac{100}{225} } \\ \frac{t}{t1} = \frac{10}{15}$

$t \: 1 = 1.5 \: t$

$\%increase = \frac{1.5t - t \times 100}{t} = 50\%$

I hope this helps ( ╹▽╹ )