In brass the velocity of longitudinal wave is 100 times the velocity of transverse wave if `Y=1xx10^11N//m^2`, then stress in the wire is

Options

A. `1xx10^(13)N//m^(2)`
B. `1xx10^(9)N//m^(2)`
C. `1xx10^(11)N//m^(2)`
D. `1xx10^(7)N//m^(2)`

Answer

B

Explanation

As `v_(L)=sqrt((Y)/(rho))andv_(T)=sqrt((T)/(mu))=sqrt((T)/(pir^(2)rho))`
`therefore (v_(L))/(v_(T))=sqrt((Y)/(rho)xx(pir^(2)rho)/(T))=sqrt((Y)/(T//pir^(2)))=sqrt((Y)/("stress"))`
`therefore` Stress `=(Y)/((v_(L)//v_(T))^(2))=(1xx10^(11))/((100)^(2))=1xx10^(7)N//m^(2)`