As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45 ° with the load axis. The length of wire is 62 . 8 cm and its diameter is 4 mm . The Young's modulus is found to be x × 10 4 N m - 2 The value of x is _______.

Step-by-step solution

Given here, L = 62 . 8   cm   and   d = 4   mm . From the given graph, we can see that extension in wire is linearly dependent on force applied. Slope of the curve is tan 45 ° = 1 . So, F = Δ L Young's modulus is given by Y = F L A Δ L , where, A is area of wire. ⇒ Y = L A ⇒ Y = 62 . 8 × 10 - 2 π 2 × 10 - 3 2 ⇒ Y = 5 × 10 4   N   m - 2