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A wire of length 2m and diameter 2cm is ...

A wire of length 2m and diameter 2cm is suspended vertically with its top end fixed. Its poisson's ratio and Young's modulus are 0.2 and `1.8 times 10^11 N.m^-2` respectively.What will be its lateral strain if a load of 1000kg is suspended at its lower end ?

Text Solution

Verified by Experts

Young modulus, `Y=(mg)/(pir^2).L/l`
`therefore` Longitudinal strain,
`l/L=(mg)/(pir^2.Y)=(1000times9.8times7)/(22times(0.01)^2times1.8times10^11)`
`[Here,r=D/2=2/2cm=1cm=0.01m]`
Again , poisson.s ratio , `sigma=(d//D)/(l//l)`
`therefore` Lateral strain ,`d/D=sigma.l/L=(0.2times1000times9.8times7)/(22times(0.01)^2times1.8times10^11)`
`=3.46 times 10^-5`
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