Question

how is the time period of simple pendulum affected if the length of the pendulum is doubled ​

Answer 1

GiveN :-

• Length of the simple pendulum is doubled .

To FinD :-

• How will be time period of simple pendulum will be affected .

SolutioN :-

Time period of a simple pendulum is given by ,

$\qquad\qquad\boxed{\red{\bf T =2\pi\sqrt{ \dfrac{l}{g}}}}$

So, it's clear that time period of asimple pendulum is directly proportional to the square root of the length .

$\tt:\implies T_1 \propto \sqrt{l} \\\\\tt:\purple{\implies T_1 = k \sqrt{l} \qquad\lgroup Original\: lenght \rgroup }$

$\rule{200}2$

$\underline{\green{\sf When\ length \ is \ doubled :- }}$

$\tt:\implies T_2 \propto \sqrt{l} \\\\\tt:\implies T_2 =k\sqrt{ \dfrac{l}{2}}\\\\\tt:\pink{\implies T =k\sqrt{\dfrac{l}{2}}}$

$\rule{200}2$

$\underline{\green{\sf On \ dividing \ them :- }}$

$\tt:\implies \dfrac{T_1}{T_2}=\sqrt{\dfrac{l}{\frac{l}{2}}} \\\\\tt:\implies \dfrac{T_1}{T_2}=\sqrt{\dfrac{2l}{l}}\\\\\tt:\implies \dfrac{T_1}{T_2}=\sqrt 2 \\\\\underline{\boxed{\red{\tt\longmapsto T_1 = \sqrt{2}T_2 }}}$

$\boxed{\green{\bf \pink{\dag} \: Hence \ the \ time \ period \ becomes \ \sqrt{2} \ times. }}$