Please solve this physics problem: The breaking stress of aluminium is 7.5 x 108 dyne/cm2 . If the density of aluminium is 2.7 g/cm3 , find the maximum of length of aluminium wire that can hang vertically without breaking.
Breaking stress σb = 7.5 x 108 dyne/cm2
ρ = 2.7 g/cc
g = 980 cm/s2
Let the maximum length that can be hung vertically be L
Let CSA = A
Volume of the wire = AL
Mass of the wire = ρAL
When hung force acting on the wire
F = ρALg
=> F/A = ρLg
=> σ = ρLg
Now the maximum stress that wire can withstand = σb so,
σ = σb
=> ρLg = σb = 7.5 x 108
=> L = 7.5 × 108/(ρg)
=> L = 7.5 × 108/(2.7×980)
=> L = 2.8× 105 cm
= 2.8× 103 m or 2.8 km