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A body of mass 4 kg and density 2.5 g.cm...

A body of mass 4 kg and density `2.5 g.cm^-3`, suspended by a metallic wire of length 1 m and diameter 2mm, is kept completely immersed in water. What will be the increase in the length of the wire? Young's modulus of the metal `=2 times 10^11 N.m^-2` and `g=9.8 m.s^-2`.

Text Solution

Verified by Experts

Volume of the body ,`V=4/(2.5times1000)=16times10^-4m^3`
Apparent weight of the body when immersed in water,
`W.=mg-Vtimes1000timesg`
`=4times9.8-16times10^-4times1000times9.8`
`=39.2-15.68=23.52N`
IF the elongation of the wire is l., then
`Y=F/A.L/l.[Here,F=W.`]
or,`l.=F/A.L/Y=(23.52times1)/(3.14times(10^-3)times2times10^11)[because radius =1mm=10^3m`]
`=3.75 times 10^-5 m`.
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