A massless rod BD is suspended by two identical massless strings AB and CD of equal lengths. A block of mass m is suspended at point P such that BP is equal to x, If the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of x is :-

Options

A. `(l)/(5)`
B. `(l)/(4)`
C. `(4l)/(5)`
D. `(3 l)/(4)`

Answer

A

Explanation

`f propv propsqrt(T)`
`f_(AB)=2f_(CD)`
`:. T_(AB)=4T_(CD)`
Further `Sigma tau_(p)=0`
`:. F_(AB)(X)=T_(CD)(l-x)`
`rArr 4X=l-X ` (as `T_(AB)=4T_(CD)`)
`rArr X = l//5`