Question

The time period of two simple pendulums are in the ratio 4: 9. Compare their effective length.​

Answer 1

Explanation:

hope it's helpful to you

Answer 2

Given: The ratio of the time period of the two simple pendulums is 4:9

Find: We have to find the effective length

Solution: We know the concept of the simple pendulum,

We have the expression of the simple pendulum,

The expression is,

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

For two pendulums both have different length and different time periods,

For 1st

$T_{1} = 2\pi\times\sqrt{\dfrac{L_{1} }{g} } ---- (1)$

For 2nd

$T_{2} = 2\pi\times\sqrt{\dfrac{L_{2} }{g} } ------ (2)$

comparing

$\dfrac{T_{1}}{T_{2}} = \dfrac{2\pi\sqrt{\dfrac{L_{1}}{g} } }{2\pi\sqrt{\dfrac{L_{2}}{g} }} \\\\\\\dfrac{T_{1}}{T_{2}} = \dfrac{\sqrt{L_{1}} }{\sqrt{L_{2}} }$

$\sqrt{\dfrac{T_{1}}{T_{2}} } = \dfrac{L_{1}}{L_{2}} \\\\\\\sqrt{\dfrac{{4}}{{9}} } = \dfrac{L_{1}}{L_{2}} \\\\\\\dfrac{2}{3} = \dfrac{L_{1}}{L_{2}}$

So, the effective length is 2:3