Question

the ratio of the lengths of two simple pendulums are 4:9 . calculate the ratio of its time period

please answer with explanation.​

Answer 1

Answer:

2:3

Explanation:

let the lengths,and time period of pendulum be l₁,T₁ and l₂,T₂

given l₁ : l₂ = 4 : 9

Time Period of pendulum=2π√l/g

so,

Time Period of pendulum ∝ √l

hence T₁ : T₂ = √l₁ : √l₂

                    =  √4:√9

                    =   2:3

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Answer 2

Answer:

The ratio of its time period is :

$T_1 : T_2 = 2 : 3$

Explanation:

Given,

The ratio of the lengths of two simple pendulums are 4:9

$\therefore \: \frac{l_1}{l_2} = \frac{4}{9}$

$\frac{T_1}{T_2} = to \: find$

we know that,

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

For first pendulums :

$T_1 = 2\pi \sqrt{ \frac{l_1}{g} } \: \: \: \: - - - (1)$

For second pendulums :

$T_2 = 2\pi \sqrt{ \frac{l_2}{g} } \: \: \: \: - - - (2)$

So,

$\sf \: eqn.(1) \div eqn.(2) \implies \: \\ \\ \: \: \: \: \frac{T_1}{T_2} = \sqrt{ \frac{l_1}{l_2} } \\ \implies \: \frac{T_1}{T_2} = \sqrt{ \frac{4}{9} } \\ \implies \: \frac{T_1}{T_2} = \frac{2}{3}$