Question

. A copper wire has a length of 2.2 m. Its diameter is7 x 10-4 m. What will be the elongation in its lengthwhen a 5 kg-weight is suspended? (Young's modulusof copper, Y = 1.25 x 1011 Nm-2 and g = 10 m s?).Ans. 2.3 mm​

Answer 1

Given

L = Length of copper wire = 2.2 m

d = Diameter of wire = $7\times 10^{-4}\ \text{m}$

Y = Young's modulus = $1.25\times 10^{11}\ \text{N/m}^2$

m = Mass attached = 5 kg

g = Acceleration due to gravity = $10\ \text{m/s}^2$

To find

Elongation of wire

Solution

Force of tension on the wire

$F=mg\\\Rightarrow F=5\times10\\\Rightarrow F=50\ \text{N}$

Elongation is given by

$\Delta L=\dfrac{FL}{AY}\\\Rightarrow \Delta L=\dfrac{FL}{\dfrac{\pi}{4}d^2Y}\\\Rightarrow \Delta L=\dfrac{50\times 2.2}{\dfrac{\pi}{4}(7\times 10^{-4})^2\times 1.25\times 10^{11}}\\\Rightarrow \Delta L=0.002286\ \text{m}\approx 0.0023\ \text{m}=2.3\ \text{mm}$

The elongation of the wire is 2.3 mm.