Q67 / 90 · JEE Main 2022 (27 Jul Shift 2) · Physics

A steel wire of length 3.2 mYS=2.0×1011 N m-2 and a copper wire of length 4.4 m YC=1.1×1011 N m-2 , both of radius 1.4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1.4 mm. The load applied, in Newton, will be: (Given π=227)

  • A
    360
  • B
    180
  • C
    1080
  • Correct answer
    D
    154

Solution

Figure

When two wires are connected end to end, the tension in them will be same.

Change in length using Hooke's law can be found as,

Y=FlA∆l⇒Δl=FlAY

Total change in length can be written as,

Δl=Δl1+Δl2   

⇒Δl=Fl1 A1Y1+Fl2 A2Y2

⇒F=Δll1 A1Y1+l2 A2Y2=1.4×10-33.2π1.4×10-32×2.0×1011+4.4π1.4×10-32×1.1×1011⇒F=1.54×102=154 N

Hence, the correct answer is option: 'D'.

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