Question

the time period of two simple pendulum of a place is in the ratio 3:2, what will be the ratio of their length​

Answer 1

9:4

Explanation:

let the length of pendulum be x and y

then ratio of length will be x:y

Now we know that time period is directly proportional to square root of the length

According to this

√x/√y =3:2

Now x/y =3²/2² =9/4

Answer 2

Answer:

Ratio of their length​ =9:4

Explanation:

Given ,

The time period of two simple pendulum of a place is in the ratio ${T_{1} }:{T_{2} } =3:2$

The ratio of their length ($L_{1} :L_{2} =?$

Relation between time and length is given by

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

So T α $\sqrt{l}$

$\frac{T_{1} }{T_{2} } =\sqrt{\frac{L_{1} }{L_{2} } }$

${\frac{L_{1} }{L_{2} } }= (\frac{T_{1} }{T_{2} } )^{2}$

ratio of their length​

${\frac{L_{1} }{L_{2} } }= (\frac{3}{2} )^{2}\\ \\ = \frac{9}{4}$

Ratio of their length​ =9:4

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