Question

A uniformly tapering conical wire is made from a material of young modulus y

Answer 1

r−Rx=3R−RLr−Rx=3R−RL

=> r=R(1+2xL)r=R(1+2xL)

Y=MgπR2dLdxY=MgπR2dLdx

dL=MgπR2dx(1+2xL)2dL=MgπR2dx(1+2xL)2

ΔL=MgYπR2∫0Ldx(1+2xL)2ΔL=MgYπR2∫0Ldx(1+2xL)2

=MgL(1+2xL)2=MgL(1+2xL)2

L′=L+ΔL=L(1+13MgπR2Y)

hope this answer helpful u