A slightly conicalwire of length l and radius r_(1) and r_(2)is stretchedby two forcesappliedparallel to length in oppositedirectionsand normal to end faces. If Y denotesthe Young.s modulus, then findthe elongationof the wire.

A slightly conicalwire of length l and radius r_(1) and r_(2)is stretc

1.	A slightly conicalwire of length l and radius r_(1) and r_(2)is stretchedby two forcesappliedparallel to length in oppositedirectionsand normal to end faces. If Y denotesthe Young.s modulus, then findthe elongationof the wire.
Answer» SOLUTION : Consideran elementof length dx at distance x asshown in FIG. The radius of the section `r_(x) =r_(1)+((r_(2)-r_(1))/(l))x` The extensiion of the element `DL=(F(dx))/( A_(x)Y)=(Fdx)/( pi r_(x)^(2)Y)` Totalextension `Deltal=int_(0)^(l)(Fdx)/(pi[r_(1)+(r_(2)-r_(1))/(l)x]^(2)Y)=(FL)/(pi r_(1)r_(2)Y)`