Question

A nylon rope of $2cm$ in diameter has a breaking strength of $1.5\times {10}^{5}N$. Find the breaking strength of rope having $1cm$ diameter?

• A. $0.375\times {10}^{5}N$
• B. $2\times {10}^{5}N$
• C. $6\times {10}^{5}N$
• D. $9\times {10}^{4}N$

Answer 1

The correct option is A $0.375\times {10}^{5}N$

As mentioned above, Breaking force $F\propto r^2$
Therefore, we can write,
$\frac{F_1}{F_2}=\frac{{r_1}^2}{{r_2}^2}$

$Given:F_1=1.5\times {10}^{5}N$

$r_1=1cm$
$r_2=0.5cm$

$F_2=\frac{{r_2}^2}{{r_1}^2}\times F_1$

$F_2=0.375\times {10}^{5}N$