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BITSAT2016PhysicsMechanical Properties of SolidsActual

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2 has cross-sectional area 3 A . If the length of wire 1 increases by x on applying force F , how much force is needed to stretch wire 2 by the same amount?

Options

  1. A4 F
  2. B6 ~F
  3. C9 F
  4. DF

Correct answer

C. 9 F

Step-by-step solution

As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection 3 A will be / 3 (same volume as wire 1 ). For wire 1, Y= F / A x / For wire 2, Y= F^ / 3 A x /( / 3) From (i) and (ii) , F A x = F^ 3 A 3 x F^ =9 F

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