A rod PQ of length 'L' is hung from two identical wires A and B. A block of mass 'm' is hung at point R of the rod as shown in figure. The value of 'x' so that the fundamental mode in wire A is in resonance with first overtone of B is

Options

A. `(4L)/(5)`
B. `(L)/(4)`
C. `(L)/(5)`
D. `(2L)/(3)`

Answer

C

Explanation

`f_(A)=2f_(B) , (1)/(2l)sqrt((T_(A))/(mu))=(2)/(2l)sqrt((T_(B))/(mu))impliesT_(A)=4T_(B)`
`vectau=vecrxxvecf=` constant, `(T_(A))/(T_(B))=4=(l-x)/(x)`