The time periods of two simple pendulums at a place are in ratio 2 : 1. What will be the ratio of their length ?

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Solution

We know that time period is directly proportion to the square root of length

so $\frac{L_{1}}{L_{2}} = \frac{T_{1}}{T_{2}^{2}}$

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

$⟶ \frac{L_{1}}{L_{2}} = \frac{4}{1}$

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The time periods of two simple pendulums at a place are in ratio 2 : 1. What will be the ratio of their length ?

We know that time period is directly proportion to the square root of length so L1L2=T1T22 ⟶L1L2=(2)2(1)2=41 ⟶L1L2=41

We know that time period is directly proportion to the square root of length

so $\frac{L_{1}}{L_{2}} = \frac{T_{1}}{T_{2}^{2}}$

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

$⟶ \frac{L_{1}}{L_{2}} = \frac{4}{1}$