The breaking stress for a metal is 7.8×109 Nm-2

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 is 7.8×10³ kgm^-3. Take g=10 Nkg^-1

Doubt by Saif

Solution : 

Let the maximum length of the wire = h_max

Breaking Stress (The maximum stress at which the wire breaks is called breaking stress of the wire)  = 7.8×10⁹ Nm^-2

We know, 
Stress = Force / Area
Stress = (Weight of the Wire) / Area
Stress = mg/A

Stress = ρVg/A [∵mass = density × volume]
Stress = ρg(A×h)/A [∵Volume = Area × height]
Stress = ρgh 

h = stress/ρg
h_max = (Maximum Stress)/ρ
h_max = [7.8×10⁹]/[7.8×10³×10]
h_max = 10⁵ m 

Hence, the required maximum length of the wire is 100000 m or 100 km.