Physics · Young's modulus, bulk modulus and modulus of rigidity

The radii and Young's moduli of two uniform wires and are in the ratio 2: 1 and

The radii and Young's moduli of two uniform wires \( A \) and \( B \) are in the ratio 2: 1 and 1: 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire \( A \) is one percent, the percentage increase in length of the wire \( B \) is:

  • A. 1.0
  • B. 1.5
  • C. 2 .0 \)
  • D. 3.0

Step-by-step solution

Given: r_A/r_B = 2, Y_A/Y_B = 1/2, same force F and same length L (assumed). ΔL = FL/(AY) ∝ 1/(r^2 Y). Ratio ΔL_A/ΔL_B = (r_B^2 Y_B)/(r_A^2 Y_A) = (1/4) * 2 = 1/2, so ΔL_B = 2ΔL_A. Percentage increase in length of B = (ΔL_B/L)*100% = 2*(ΔL_A/L)*100% = 2*1% = 2%.
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