Question

Four wires of same material and of dimensions as mentioned below are stretched by a load of same magnitude separately. Which one of them will be elongated maximum?

• A. Wire of 1 m length and 2 mm diameter
• B. Wire of 2 m length and 2 mm diameter
• C. Wire of 3 m length and 1.5 mm diameter
• D. Wire of 1 m length and 1 mm diameter

Answer 1

The correct option is D. Wire of 3 m length and 1.5 mm diameter.

The elongation in the wire is given by,

$\Delta l=\frac{Fl}{AY}$

Since material and tension in the wire is the same for all.

$⟹\Delta l\propto \frac{l}{A}\propto \frac{l}{d^2}$

where $l$ is the length of wire and $d$ is the diameter.

Putting the values, we get elongation is maximum in the wire of option D.