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A rubber cord of length 20 m is supplied...

A rubber cord of length 20 m is supplied from a rigid support by one of its ends it hangs vertically. What will be the elongation of the cord due to its own weight? The density of rubber=`1.5 g.cm^-3` and Young 's modulus=`49 times 10^7 N.m^-2`.

Text Solution

Verified by Experts

Here the downward force,
F=weight of the chord
=volume of the cord `times` density`times` acceleration due to gravity
`=20timesAtimes1.5times1000times9.8N`[A= area of cross section of the cord]
The centre of gravity of the rubber cord is at a vertical distance of 10 m from the fixed end. The weight of the cord acts through its centre of gravity. Hence the length of the upper half, above the centre of gravity , is taken as the initial length to estimate the elongation of the cord. So, L=10m.
`thereforeY=(FL)/(Al)`
or,`l=(FL)/(AY)=(20timesAtimes1.5times1000times9.8times10)/(A times 49times10^7)=0.006m`
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