Two strings A and B of lengths,`L_A=80 cm` and `L_B=x cm` respectively are used separately in a sonometer. The ratio of their densities `(rho_A//rho_B)` is 0.81. The diameter of B is one-half that of A.if the strings have the same tension and fundamental frequency the value of x is

Options

A. 33
B. 102
C. 144
D. 130

Answer

C

Explanation

`n=1/(2l)sqrt(T/m)=1/(2l)sqrt(T/(pir^2rho)`
`n_A=1/(2L_A)sqrt(T/(pir_A^2rho))`,`n_B=1/(2L_B)sqrt(T/(pir_B^2rho))`
`:. n_A=n_B`,`T_A=T_B`
`1/(2L_A)sqrt(T/(pir_A^2rho))=1/(2L_B)sqrt(T/(pir_B^2rho)`
`L_A/L_B=sqrt((pir_A^2rho_A)/((pir_B^2rho_B)))`
`x/80sqrt(4xx0.81)`
`x=80sqrt(3.24)=144cm`