A steel wire can support a maximum load of W before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?

Options

A. `W `
B. `(W)/(2)`
C. `(W)/(4)`
D. `4W`

Answer

C

Explanation

Breaking force = Breaking stress `xx` Area of cross section .
for given material of the wire, breaking stree is constant .
`therefore (F_(1))/(A_(1)) =(F_(2))/(A_(2))`
`F_(2) = F_(1) ((A_(2))/(A_(1))) = F_(1)((A_(1)//4)/(A_(1))) = (F_(1))/(4) = (W)/(4)" "(because r_(2) = r_(1//2))`