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 seaction
For given material of the wire, breaking stress is constant.
`(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)`