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A wire loaded by a weight of density 7.6...

A wire loaded by a weight of density `7.6 g cm^(-3)` is found to measure `90 cm`. On immersing the weight in water, the length decreases by `0.18 cm`. Find the original length of wire.

Text Solution

Verified by Experts

The correct Answer is:
`88.632cm`
`rho = 7.6 g//cm^(3)`
`l + Deltal = 90 cm`
`Deltal = (wl)/(AY) ….(1)`
`Deltal - 0.18 = ((w - (w)/(rho_(0))rho_(l))l)/(AY) …..(2)`

`(Deltal - 0.18)/(Deltal) = 1 - (rho_(l))/(rho_(0))`
`1 - (0.18)/(Deltal) = 1-(1)/(7.6)`

`Deltal = 7.6 xx 0.18`
then `l + Deltal = 90`
`l = 90 - 7.6 xx 0.18 = 88.632 cm`
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Knowledge Check

  • A wire is loaded by a weight of density 9g//cm^(3) and stretched to a length of 98 cm. On immersing the weight in water the length shortens by 2.5 mm. Then the original length of the wire will be [rho_(w)=1 gm//cm^(3)]

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