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Two partical tied to different strings a...

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 period is:

A

`sqrt((3)/(2))`

B

`sqrt((2)/(3))`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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))`.
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