Question

If the length of a simple pendulum increases by 5%, then its period shall increase by ______.

Options

• 25%

• 2.24%

• 2.5%

• 5%

Answer 1

If the length of a simple pendulum increases by 5%, then its period shall increase by 2.5%.

Explanation:

T = `2p sqrt(l/"g"), "T'" = 2pi sqrt(105/100)"l"/"g" = 1.025 xx 2pi sqrt("l"/"g")`

% change = `(Delta "T")/"T" xx 100 = ("T'" - "T")/"T" xx 100`

`= (.025 xx 2pi sqrt("l"/"g") xx 100)/(2pi sqrt("l"/"g"))`

= 2.5 %