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An aluminium wire is clamped at each end...

An aluminium wire is clamped at each end and under zero stress at room temperature. Temperature of room decreases resulting into development of thermal stress & thermal strain in the wire. Cross-sectional area of the wire is `5.00 xx10^(-6)m^(2).` Density of aluminium is `2.70 xx10^(3) kg//m^(3).` Young’s modulus of aluminium is `7.00 xx10^(10) N//m^(2).` A transverse wave speed of 100 m/s generates in the wire due to a resulting thermal strain `((Deltal)/(l))` developed in the wire. The thermal strain `((Delta l )/(l))` is: (l is original length of the wire)

A

`3.86 xx 10^(-4)`

B

`2.86 xx 10^(4)`

C

`3.42 xx 10^(-4)`

D

`2.42 xx 10^(-4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Young.s modulus `Y=(T//A)/(Delta l//l), (Delta l)/(l)= (T)/(YA)`
Wave speed `v= sqrt((T)/(mu))= sqrt((T)/(rho A)) therefore T= rho AV^(2)`
`therefore (Delta l)/(l) = (rho V^(2))/(Y) = (2.70 xx 10^(3) xx 10^(4))/(7.00 xx 10^(10)) = 3.86 xx 10^(-4)`
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