Question

A metal rod is tied vertically. If the breaking stress is 5.4 × 10⁹ Nm² and density 5.4 × 10³ kg/m³. Find the maximum length of rod that can be held without breaking.

Answer 1

Stress = \(\frac{F}{A}\)

= \(\frac{Mg}{A}\) 

[∵\(\frac{M}{AL}\) = ρ]

= ρgL

If ρgL > Maximum stress that it can sustain than the rod break. 

So, ρgL < 5.4 × 10⁹ Nm^-2

l< \(\frac{5.4 \times 10^{9}} {5.4 \times 10^3\times (10ms^{-1})}\)

l < 10⁵ m

Maximum length of wire is 105 m or 100 km.