In the sonometer experiment , a tuning fork of frequency `256 Hz` is in resonance with `0.4 m` length of the wire when the iron load attached to free end of wire is `2 kg`. If the load is immersed in water , the length of the wire in resonance would be ( specific gravity of iron ` = 8`)

Options

A. 0.37m
B. 0.43m
C. 0.31m
D. 0.2m

Answer

A

Explanation

`sqrtT prop sqrtl impliessqrt(T_1/T_2)=l_1/l_2 implies l_2=l_1 times sqrt(T_2/T_1)`
`l_1 times sqrt((rho_1vg-p_2 vg)/(rho_1Vg))=l_1 sqrt(1-rho_2/rho_1)=0.4 timessqrt(1-1/8)`
`implies 0.4 times sqrt(7/8)=0.37`