Question

if time period of a pendulum increases to 1.4142 times it's initial value ,then the length would have changed to ( show the working give info)

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Answer 1

Answer:

5.82836 times

Explanation:

$t = 2\pi \sqrt{ \frac{l}{g} } \\ t \: increases \: to \: 1.4142 \: times \\ so \: it \: will \: become \: 2.4142 \\ let \: new \: l \: be \: x \\ so \: 2.4142t = 2\pi \sqrt{ \frac{x}{g} } \\ on \: dividng \: \frac{t}{2.4142t} \: we \: get \\ \frac{t}{2.4142t} = \frac{2\pi \sqrt{ \frac{l}{g} } }{2\pi \sqrt{ \frac{x}{g} } } \\ \frac{1}{2.4142} = \frac{ \sqrt{l} }{ \sqrt{x} } \\ \frac{(1) ^{2} }{(2.4142) {}^{2} } = \frac{l}{x} \\ \frac{1}{5.828} = \frac{l}{x} \\ x = 5.82836l \: is \: the \: answer$