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. `10^(7) N//m^(2)`
B. `10^(8) N//m^(2)`
C. `10^(9) N//m^(2)`
D. `10^(10) N//m^(2)`

Answer

A

Explanation

`V_(L) = sqrt((E)/(rho)) = sqrt((Y)/(rho)), V_(Tr) = sqrt((T)/(m)) = sqrt((Mg)/(pir^(2) rho))`
`:. (V_(L))/(V_(Tr)) = sqrt((Y)/(rho) xx (pi r^(2) rho)/(Mg)) = sqrt((Y)/((Mg)/(pir^(2)))) = sqrt((Y)/("Stress"))`
`:. ((V_(L))/(V_(T)))^(2) = (Y)/("Stress") :. 10^(4) = (10^(11))/("Stress")`
`:. "Stress" = 10^(7) N//m^(2)`