Answer:
0.3 mm
Explanation:
[tex]\rho[/tex] = Density of material
[tex]\mu[/tex] = Linear density of the material = [tex]\rho A[/tex]
Area = Area = [tex]\pi r^2[/tex]
r = Radius
The velocity of a wave is given by
[tex]v=\sqrt{\dfrac{T}{\mu}}\\\Rightarrow v=\sqrt{\dfrac{T}{\rho A}}\\\Rightarrow v=\sqrt{\dfrac{T}{\rho \pi r^2}}[/tex]
It can be seen that the velocity is inversly proportional to the radius
[tex]v\propto \sqrt{\dfrac{1}{r^2}}\\\Rightarrow v\propto \dfrac{1}{r}[/tex]
So,
[tex]\dfrac{v_a}{v_b}=\dfrac{r_b}{r_a}[/tex]
From the question
[tex]v_b=\dfrac{1}{3}v_a[/tex]
[tex]\\\Rightarrow \dfrac{v_a}{\dfrac{1}{3}v_a}=\dfrac{r_b}{0.1}\\\Rightarrow 3=\dfrac{r_b}{0.1}\\\Rightarrow r_b=3\times 0.1\\\Rightarrow r_b=0.3\ mm[/tex]
The radius of wire B is 0.3 mm
