A wire of radius r stretched without tension along a straight line is tightly fixed at A and B. What is the tension in the wire when it is pulled in the shape ACB? Assume Young's modulus of material of the wire to be Y.

A wire of radius r stretched without tension along a straight line is

1.	A wire of radius r stretched without tension along a straight line is tightly fixed at A and B. What is the tension in the wire when it is pulled in the shape ACB? Assume Young's modulus of material of the wire to be Y.
Answer» Solution : LET 2L be the original length of wire AB, i.e., L = 2l, when wire is pulled into shape ACB, the INCREASE in length, `DeltaL=(AC+CB)-AB` `=2(l^(2)+d^(2))^(1//2)-2l` longitudinal strain `=(DeltaL)/(L)` `=(2(l^(2)+d^(2))^(1//2)-2l)/(2l)` `=(2l[1+((d^2)/(l^2))^(1//2)-1])/(2l)` `=[1+(1)/(2)(d^2)/(l^2)-1]=(d^2)/(2l^2)` longitudinal stress `=("tension")/("area")=(F)/(pir^2)` `THEREFORE` Young's modulus, `Y=("longitudinal stress")/("longitudinal strain")` `(F//pir^2)/(d^2//2l^2)` `therefore` Tension in the wire `F=Yxxpir^(2)xx(d^2)/(2l^2)`