Two elastic rods of equal natural length are connected in parallel between two rigid plates. Rod 1 has cross-sectional area A and Young's modulus Y. Rod 2 has cross-sectional area 2A and Young's modulus Y/2. A total tensile force P is applied symmetrically to the outer plate so that both rods undergo the same elongation. What force is carried by rod 1?
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Question

Two elastic rods of equal natural length are connected in parallel between two rigid plates. Rod 1 has cross-sectional area A and Young's modulus Y. Rod 2 has cross-sectional area 2A and Young's modulus Y/2. A total tensile force P is applied symmetrically to the outer plate so that both rods undergo the same elongation. What force is carried by rod 1?

Options

G1 Physics · Accepted Answer

Because the rods are connected in parallel between rigid plates, both rods have the same strain ε. For rod 1, F₁ = YAε. For rod 2, F₂ = (Y/2)(2A)ε = YAε. Thus, F₁ = F₂. The total applied force is P = F₁+F₂ = 2F₁. Hence, F₁ = P/2. Correct option: C.