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. four times that of A
B. two times that of A
C. three times that of A
D. same as that of A

Answer

A

Explanation

Stress (s) `= ("Force")/("Area")` and `r_(A) = 2r_(B)`
`:. S_(A) = (F)/(pi(r_(A))^(2))` and `S_(B) = (F)/(pi (r_(B))^(2))`
`(S_(B))/(S_(A)) = (F)/(pi (r_(B))^(2)) xx (pi (r_(A))^(2))/(F)`
`= ((r_(A))/(r_(B)))^(2) = ((2r_(B))/(r_(B)))^(2) = 4`
`:. S_(B) = 4S_(A)`