The lenghts of two simple pendula are in the ratio of `2:3` and the ratio of the acceleration due to gravity at the two places where they are set up is `3:2` . The ratio of their frequencies is

Options

A. `3:2`
B. `4:9`
C. `9:4`
D. `2:3`

Answer

D

Explanation

`l_(A) =l-x`
`l_(B) = l +x`
`" Where " l =100 cm`
`l_(A) lt l_(B)`
`T_(A) lt T_(B)`
`_(T_(B))/(T_(A)) =(4)/(3)`
`:. Sqrt((l_(B))/(l_(A))) =(T_(B))/(T_(A))`
`(l+x)/(l-x) =(16)/(9) .(l)/(x)= (25)/(7)`
`x= (7)/(25)xx 100=28cm`
Higher frequency `rArr` lower time period Regular
shorter pendulum = pendulum A
`:. `length of pendulum A=100 -28 =72 cm