Two wires A and B made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 × 10⁻⁵ m² and 4.5 × 10⁻⁵ m², respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x i $s ______.$
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Question

Two wires A and B made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 × 10⁻⁵ m² and 4.5 × 10⁻⁵ m², respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x i $s ______.$

Options

G1 Physics · Accepted Answer

Young's modulus is Y = stress/strain = (F/A)/(ΔL/L) = FL/(AΔL). The two wires are stretched by the same load and undergo the same extension. Therefore, Y(A)/Y(B) = [L(A)/A(A)]/ [L(B)/A(B)] = [L(A)A(B)]/ [L(B)A(A)]. Substitute: L(A) = 6.0 cm, L(B) = 5.4 cm, A(A) = 3.0×10⁻⁵ m², A(B) = 4.5×10⁻⁵ m². Thus, Y(A)/Y(B) = [6.0×4.5]/[5.4×3.0] = 27/16.2 = 5/3. The question gives Y(A):Y(B) = x:3. Therefore, x = 5. Correct option: D.