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A rubber cord of length 10 m is suspende...

A rubber cord of length 10 m is suspended vertically. How much does it stretch under its own weight? Density of rubber `=1.5 times 10^3 kg .m^-3`, Young's modulus of rubber `=6 times 10^6 gf.cm^-2`, g=`9.8 m.s^-2`

Text Solution

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Given L=10m,`rho=1.5 times 10^3 kg.m^-3`,
`Y=6 times 10^6 gf .cm^-2=6 times 10^6 times 980 dyn . Cm^-2`
`=5.88 times 10^8 N.m^-2`
Let a be the area of cross section of the rubber cord. Then F=weight of the rubber cord
`L=a times rho times g`
The weight of the rubber cord acts at its centre of gravity and hence the weight of the rubber cord will produce extension in the length `L/2` of the chord.
Now,`Y=(F(L/2))/(al)or,l=(F times L)/(2a timesY)`
`l=(Larhog times L)/(2a times Y)=(L^2rhog)/(2Y)=(10^2times1.5times10^3times9.8)/(2 times 5.88 times 10^8)`
`=1.25 times 10^-3m=1.25mm`.
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