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((2)/(3))`
C. 1
D. None of these

Answer

B

Explanation

Since `T=2pisqrt((Lcostheta)/(g))`
:. `T_(1)=T_(2)`
implies `L_(1)costheta=L_(2)costheta_(2)`
`:. (L_(1))/(L_(1))=(costheta_(2))/(costheta_(1))=(cos45^(@))/(cos30^(@))`
`(L_(1))/(L_(2))=(sqrt(2))/(sqrt(3))`