Question

A force $ F $ is required to break a wire of length $ I $ and radius $ r $ . What force is required to break a wire, of same material having twice the length and six times the radius?

• A. $ F $
• B. $ 3F $
• C. $ 9F $
• D. $ 36F $

Answer 1

Answer: (D)

Breaking force does not depend upon length. Breaking force $=$ Breaking stress $\times$ area of cross-section and breaking stress is constant for a given material.
$\because$ Breaking force $\propto$ area of cross-section
$\frac{F_{2}}{F_{1}}=\frac{A_{2}}{A_{1}}=\frac{T_{1}(6 r)^{2}}{T_{1} r^{2}}=36$
or $F_{2}=36 F_{1}=36 F$