Question

The breaking stress of aluminium is 7.5 × 10⁸ dyne cm^-2. Find the greatest length of aluminium wire that can be hang vertically without breaking. Density of aluminium is 2.7 g cm^-2. (Take g = 980 cm s^-2)

Answer 1

Given :

Breaking stress = 7.5 × 10⁸ dyne cm^-2,

Ρ = 2.7 g cm^-3.

Suppose l be the greatest length of the wire that can be hang vertically without breaking.

Mass of wire,

w = Area of cross-section × Length × Density = Alρ

Hence, weigh of wire,

w = mg = Alρg

This is equal to the maximum force that the wire can withstand.

So, breaking stress = \(\frac{W}{A}\) = \(\frac{Alρg}{A}\) = lρg

or 7.5 × 10⁸ = l × 2.7 × 980

So, l = \(\frac{7.5 × 10^8}{2.7×980}\)

= 2.834 × 10⁵ cm

= 2.834 km.