A simple pendulum of length `l_(1)` has frequency 1/4 Hz and another simple pendulum of length `l_(2)` has frequency 1/3 Hz. Then time period of pendulum of length `(l_(1)-l_(2))` is

Options

A. 5 s
B. 1 s
C. `sqrt(7) s`
D. `sqrt(12) s`

Answer

C

Explanation

`(n_(2))/(n_(1))=sqrt((l_(1))/(l_(2)))`
`(3)/(4)=sqrt((l_(1))/(l_(2)))`
`(9)/(16)=(l_(1))/(l_(2)) therefore (l_(2))/(l_(1))=(16)/(9)`
`(l_(2)-l_(1))/(l_(1))=(16-9)/(9)=(7)/(9)`
`sqrt((l_(1)-l_(2))/(l_(1)))=sqrt(7)/(3) therefore T_(1)-T_(2)" is "sqrt(7)`.