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Stress-Strain Graph

A force F is ...

Question

A force F is required to break a wire of length l 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

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B

3F

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C

9F

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D

36F

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Solution

The correct option is D 36F
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.
$∵$ 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 $F_{2} = 36 F_{1} = 36 F$

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