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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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