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  4. A 100 N force stretches the length of a hanging wire by 0.5 mm. The force required to stretch a wire, of the same material and length but having four times the diameter, by 0.5 mm is

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Q. A $100 \,N$ force stretches the length of a hanging wire by $0.5 \,mm$. The force required to stretch a wire, of the same material and length but having four times the diameter, by $0.5 \,mm$ is

Mechanical Properties of Solids

Solution:

As, $Y=\frac{F \times 4 \times 1}{\pi D^{2} \Delta l}$
In the given problem, $F \propto D^{2} .$ Since, $D$ is increased by a factor of 4 therefore, $F$ is increased by a factor of $16 .$ So, $F$ will be $100 \times 16=1600 \,N$