Two partical tied to different strings are whirled in a horizontal circle as shown in figure. The ratio of lengths of the string so that they complete their circular path with equal time priod is:

Options

A. `sqrt(3/2)`
B. `sqrt(1/3)`
C. 1
D. `sqrt3`

Answer

A, C

Explanation

`T sin theta=mromega^(2),Tcostheta=mg`
`:. tantheta=(romega^(2))/g` But `r=L sin theta`
`(sintheta)/(costheta) = (L sin theta xx omega^(2))/g`
`:.` Since `'omega'` is contant `L prop 1/cos theta`
`:. L_(1)/L_(2)=(costheta_(2))/(cos theta_(1))`