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Manipal MET2019PhysicsMechanical Properties of Solids

Two wires A and B are of same materials. Their lengths are in the ratio 1: 2 and diameters are in the ratio 2: 1 . When stretched by force F_A and F_B , respectively, they get equal increase in their lengths. Then the ratio F_A F_B should be

Options

  1. A1: 2
  2. B1: 1
  3. C2: 1
  4. D8: 1

Correct answer

D. 8: 1

Step-by-step solution

Young's modulus, Y= F L r^2 L Both wires are of same material. So, Y₁=Y₂ Here, aligned F_A L_A r_A^2 L_A & = F_B L_B r_B^2 L_B L_A & = L_B F_A F_B & = L_B L_A ( r_A r_B )^2 & = 2 1 ( 2 1 )^2= 8 1 F_A: F_B & =8: 1 aligned

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