Two steel wires are connected together, end to end, and attached to a wall as sh

Question

Two steel wires are connected together, end to end, and attached to a wall as shown below. The two wires have the same length and elastic modulus, but the ratio of the radius of the first wire to the radius of the second wire is 9 : 3. As the wires are initially the same length, the midpoint of the combination coincides with the connection point. An applied force then stretches the combination by 1.700 mm while the two wires stay connected together. After the wires are stretched, what is %u03B4, the

distance from the midpoint to the connection point?

Explanation / Answer

since change in entire length just depends inversely on the area of cross section as rest issues are same for both the wires

ler the radius of 1st wire be 9r

so radius of 2nd wire is 3r

area of cross section of 1st wire=pie*(9r)*(9r)=81pier^2

similarly are of cross section f 2nd wire =9pier^2

since change in length is inversly proportional to area

so if change in length in 1st wire is x

then change in length of 2nd wire is 9x

given total increase is 1.7mm so x+9x=1.7mm

so x comes out to be 0.17mm

now the midpoint is at a distance of (2L+1.7)/2 from the wall

and the connection point is at a distance of L+x=L+0.17

so the distance between midpoint and connection point is=0.85-0.17=0.68mm

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