Question

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.?

• A. $W$
• B. $\frac{W}{2}$
• C. $\frac{W}{4}$
• D. $4W$

Answer 1

Answer: (C)

$\frac{W}{4}$

Breaking stress remains constant,

$Stress=\frac{W}{A}=\frac{W}{\pi r^2}$. . . . . .(1)

Now, $r^{\prime }=\frac{r}{2}$

$Stress=\frac{W^{\prime }}{\pi r^{\prime 2}}=\frac{4W^{\prime }}{\pi r^2}$. . . . .(2)

From equation (1) and (2), we get

$\frac{W}{\pi r^2}=\frac{4W^{\prime }}{\pi r^2}$

$W=4W^{\prime }$

$W^{\prime }=\frac{W}{4}$

The correct option is C.