First slide

Elastic behaviour of solids

Question

A nylon rope 2 cm in diameter has a breaking strength of 1.5 x 10⁵ N. The breaking strength of a similar rope 1 cm in diameter is

Easy

A

$0.375 \times 10^{5} N$
B

$2 \times 10^{5} N$
C

$6 \times 10^{5} N$
D

$9 \times 10^{4} N$

Solution

Breaking strength = Breaking stress $\times \frac{{πD}^{2}}{4}$
Breaking stress is unchanged.
D is halved. So, breaking strength becomes one-fourth, i.e.,
$\frac{1}{4} \times 1 .5 \times 10^{5} N or 0 .375 \times 10^{5} N$

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