Question

1. A copper wire is secured between two immovable supports so that it has negligible tension at a temperature of300 The tension in the wire increases o 400N when it is cooled to100 c Find the diameter of the wire. For copper, a 1.70 x 10 c and Y 11.0x 101° Pa. (a) 2.61 mm 3.20 mm3.69mm (d) 4.13 mm (e) 4.52 mm (c))3.69 mrm

Answer 1

Young's modulus ---(1)

stress T/A T I strain . У/I π,2ΔΙ Y _

Where T is tension in the wire, is the radius of the wire, is the original length of wire , $\Delta l$ is the change in length of wire

$l'=l(1+\alpha \Delta T)$ ( $\Delta T$ is the change in temperature of wire)

$\frac{l'-l}{l}=(\alpha \Delta T)$

(a▲T)

$\frac{l}{\Delta l}=\frac{1}{(\alpha \Delta T)}$----(2)

From equations (1) an d(2)

T 1

$r=\sqrt{\frac{400}{\pi (11.0*10^{10})(1.70*10^{-5}) (30-10)}}=0.001845\,m$

Diameter of wire is

d _ 2Y-2 * 0.001 845 772 0.00369 m 3.69 mm

Answer is

(С.) 3.69771771