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A brass wire of cross-sectional are 2mm^...

A brass wire of cross-sectional are `2mm^(2)` is suspended from a rigid support and a body of volume `100cm^(3)` is attached to its other end. If the decrease in the length of the wire is 0.11mm, when the body is completely immeresd in water, find the natural length of the wire. `(Y_(brass)=0.91xx10^(11)Nm^(-2),rho_(water)=kg ^(-3.)`

Text Solution

Verified by Experts

Area of cross section, `A=2mm^(2)=2xx10^(-6)m^(2)`
Volume of body, `V=100"cc"=100xx10^(-6)m^(3)`
Decrease in length, `e.=0.11mm=0.11xx10^(-3)m`
Youngs modulus of brass, `Y=0.91xx10^(11)`
`N//m^(2)`
Density of water, `rho=1000kg//m^(3)`
`"Use e."=(Vrhogl)/(AY)`
Natural length of wire, `l=(e.AY)/(Vrhog)`
`=(0.11xx10^(-3)xx2xx10^(-6)xx0.91xx10^(11))/(100xx10^(-6)xx1000xx9.8)`
`thereforel=(0.2002xx10^(2))/(9.8)=(20.02)/(9.8)=2.043m`
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