A and B are two wires. The radius of A is twice that of B. They are stretched by the some load. The the stress on B is

Options

A. equal to that of A
B. two times that of A
C. four times that of A
D. half that of A

Answer

C

Explanation

Stress `= (F)/(A)`
Let r be the radius of B.
For A, `(F)/(pi(2r)^(2)) = (F)/(pi(4r)^(2))` For B, Stress `= (F)/(pi r^(2))`
`:. (F)/(pi r^(2)) = 4[(F)/(pi r^(2))]` Stress on B = 4 (Stress on A)