Question

at a certain place, length of the second's pendulum is 0.992m. Find the length of a pendulum whose time period is 1.2 seconds at the same place
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Answer 1

▶ Solution :

Given :

▪ Length of a second pendulum = 0.992m

To Find :

▪ Length of a pendulum whose time period is 1.2s at the same place.

Concept :

✏ Time period of a simple pendulum is defined as time requires to complete one oscillation.

✏ Time period of a second pendulum = 2s

✏ Formula of time period of simple pendulum in terms of length of pendulum and gravitational acceleration is given by

$\boxed{\bf{\pink{T=2\pi\sqrt{\dfrac{L}{g}}}}}$

• T denotes time period
• L denotes length of pendulum
• g denotes gravitational acceleration

Calculation :

▪ Since, gravitational acceleration is constant we can say that...

$\implies\bf\:T\propto\sqrt{L}\\ \\ \implies\sf\:\dfrac{T_1}{T_2}=\sqrt{\dfrac{L_2}{L_1}}\\ \\ \implies\sf\:\dfrac{2}{1.2}=\sqrt{\dfrac{L_2}{0.992}}\\ \\ \implies\sf\:{L_2}=0.992\times 1.28\\ \\ \implies\boxed{\bf{\purple{L_2=1.27\:m}}}$