First slide

Elastic Modulie

Question

A wire of area of cross-section 3.0mm² and natural length 50 cm is fixed at one end and a mass of 2.1 kg is hung from the other end. Young's modulus of the material of wire is 1.9 x 10¹¹ N / m² . Take g =10m / s². The potential energy stored in the wire in steady state will be

Moderate

A

$1 \cdot 9 \times 10^{- 5} J$
B

$1 \cdot 9 \times 10^{- 4} J$
C

$9 \cdot 1 \times 10^{- 4} J$
D

$9 \cdot 1 \times 10^{- 5} J$

Solution

Tension in the wire
T =mg=(2.1)(10) = 21 newton
Stress = T / A = 21N / 3.0 mm²
$= 7 \cdot 0 \times 10^{6} N / m^{2}$
Strain =Stress / Y =3.7 x 10^-5
Volume of wire
V= (3 .00 mm²) (5o cm)
$= 3 \cdot 0 \times 10^{- 6} m^{2} \times 0 \cdot 50 m = 1 \cdot 5 \times 10^{- 6} m^{3}$
$\begin{array}{l} U = \frac{1}{2} \times stress \times strain \times volume \\ = 1 \cdot 9 \times 10^{- 4} J \end{array}$

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