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

B

Explanation

T sin `theta = mr omega^(2) , T "cos" theta = "mg" `
`therefore " "` tan `theta = (romega^(2))/(g)` But r = L sin `theta`
`("sin" theta)/("cos" theta)= (L "sin" theta xx omega^(2))/(g)`
`therefore` Since `'omega'` is constant `L prop (1)/("cos" theta )`
`therefore (L_(1))/(L_(2)) = ("cos" theta_(1))/("cos" theta_(1))`