The breaking stress of aluminium is 7.5 × 108 dyne cm-2. Find the gre

1.	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» 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.

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»

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.