find the ratio of of time peroid of two pendula whaose lenghths are in ratio of 1:4

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Solution

$S i n c e, T = 2 π \sqrt{\frac{l}{g}}, w h e r e l i s t h e l e n g t h o f t h e p e n d u l u m . S i n c e, l_{1} : l_{2} = 1 : 4 S o, \frac{T_{1}}{T_{2}} = \frac{2 π \sqrt{\frac{l_{1}}{g}}}{2 π \sqrt{\frac{l_{2}}{g}}} = \frac{1}{2}$

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find the ratio of of time peroid of two pendula whaose lenghths are in ratio of 1:4

Since, T = 2 π lg , where l is the length of the pendulum.Since, l1 : l2 = 1 :4 So, T1T2 = 2 π l1g2 π l2g = 12

$S i n c e, T = 2 π \sqrt{\frac{l}{g}}, w h e r e l i s t h e l e n g t h o f t h e p e n d u l u m . S i n c e, l_{1} : l_{2} = 1 : 4 S o, \frac{T_{1}}{T_{2}} = \frac{2 π \sqrt{\frac{l_{1}}{g}}}{2 π \sqrt{\frac{l_{2}}{g}}} = \frac{1}{2}$