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 = 2pi sqrt((L cos theta)/(g))`
`:. T_(1)=T_(2)`
`rArr L_(1)cos theta_(1)=L_(2) cos theta_(2)`
`:. (L_(1))/(L_(2)) = (cos theta_(2))/(cos theta_(1))=(cos 45^(@))/(cos 30^(@))`
`(L_(1))/(L_(2))= (sqrt(2))/(sqrt(3))`.