Answered

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find the ratio of the lengths of the two mathematical pendulums, if the ratio of periods is 1.5​

Sagot :

Answer:

The ratio of lengths of the two mathematical pendulums is 9:4.

Explanation:

It is given that,

The ratio of periods of two pendulums is 1.5

Let the lengths be L₁ and L₂.

The time period of a simple pendulum is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

or

[tex]T^2=4\pi^2\dfrac{l}{g}\\\\l=\dfrac{T^2g}{4\pi^2}[/tex]

Where

l is length of the pendulum

[tex]l\propto T^2[/tex]

or

[tex]\dfrac{l_1}{l_2}=(\dfrac{T_1}{T_2})^2[/tex] ....(1)

ATQ,

[tex]\dfrac{T_1}{T_2}=1.5[/tex]

Put in equation (1)

[tex]\dfrac{l_1}{l_2}=(1.5)^2\\\\=\dfrac{9}{4}[/tex]

So, the ratio of lengths of the two mathematical pendulums is 9:4.

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