Question

Four uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has :

• A. radius $3mm$, length $3m$
• B. radius $0.5mm$, length $0.5m$
• C. radius $2mm$, length $2m$
• D. radius $3mm$, length $2m$

Answer 1

The correct option is D radius $3mm$, length $2m$

According to Young's modulus of elasticity:
$\Delta l=\frac{Fl}{\pi r^{2}Y}$
$\Delta l\propto 1/r^2$
Hence only option "D" is satisfying the relation.