Question

The breaking stress for a metal is 7.8 × 10⁹ Nm^–2. Calculate the maximum length of the wire made of this metal which may be suspended without breaking. The density of the metal = 7.8 × 10^–3 kg m^–3. Take g = 10 N kg^–1.

Answer 1

Breaking stress = Maximum stress that the wire can withstand 

= 7.8 × 10⁹ Nm^–2 

When the wire is suspended vertically, it tends to break under its own weight. 

Let its length be I and cross-sectional area A. 

Weight of wire = mg = volume × density × g = Alρg

For the wire not to break, lρg = Breaking stress = 7.8 × 10⁹ Nm^–2