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A force of 10^6 N.m^-2 is required for b...

A force of `10^6 N.m^-2` is required for breaking a material. IF the density of the material is `3 times 10^3 kg.m^-3`, then what should be the length of the wire made of this material , so that it breaks due its own weight? [`g=9.8 m.s^-2`]

Text Solution

Verified by Experts

Let L be the length of the wire which will break under its own weight.IF a is the cross section and `rho` is the density of the material of the wire, then ,
breaking weight=`a times L times rho times g`
`= a times L times 3 times 10^3 times 9.8`.......(1)
[Here `rho=3 times 10^3 kg.m^-3,g=9.8 m.s^-2`]
Also, breaking stress=`10^6 N.m^-2`
Therefore, breaking weight `=10^6 times a`...........(2)
From equations (1) and (2) we have,
`a times L times 3times10^3times9.8=10^6timesa`
or,`L=10^6/(3times10^3times9.8)approx34m`
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