Question

the period of simple pendulum is doubled when its length increases 0.9 metre then what will be the original length of Pendulum​

Answer 1

Answer:

Orignal length of pendulum = 0.3 meter

Explanation:

As we know period of a pendulum

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

if we simplify it for approx. estimation the value of "pi" would cancel the "square root of g" which have near values, hence it become

$t = 2 \sqrt{l}$

Now as given in the question the period become double when length increase by 0.9, thus

$2t = 2\sqrt{l + 0.9}$

it implies that

$t = \sqrt{l + 0.9}$

comparing both the values of t

$2 \sqrt{l} = \sqrt{l + 0.9}$

squaring both sides, gives

$4l = l + 0.9$

thus

$4l - l = 0.9$

and

$l = \frac{0.9}{3} = 0.3 \: m$