Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is ____ x 10^-6m. [Young’s modulus for steel = 2 x 10¹¹Nm^-2 , $π = 3.14$ and g = 10ms^-2].

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answer is 20.

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Detailed Solution

Tension in steel wire, T₁=2g+T₂

T₂ = 1.14g = 11.4N

T₁ = 20+11.4=31.4N
Young modulus of steel, $Y = \frac{\frac{T_{1}}{A}}{\frac{ΔL}{L}}$
Elongation in steel wire $ΔL = \frac{T_{1} L}{AY}$
$ΔL = \frac{31.4 \times 1.6}{π {(0.2 \times 10^{- 2})}^{2} \times 2 \times 10^{11}} = \frac{16}{2 \times 4 \times 10^{- 6} \times 10^{11}}$
= 20 x 10^-6 m