Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
