Verified Solution • 2025–26 Session moderate

QJEEM20Ph4824: JEE Main 2020 Physics - Class 11 JEEM20Ph4824 Solution: Speed of a transverse wave on a straight wire (mass 6.0 g,…

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 ×\times 1011 Nm-2, the extension of wire over its natural length is :

Multiple Choice Options

  • A 0.03 mm
  • B 0.04 mm
  • C 0.02 mm
  • D 0.01 mm

Step-by-Step Verified Solution

Velocity of the wave, v = Tμ\sqrt {{T \over \mu }}

⇒\Rightarrow T = v2 μ\mu

We know, Youngs modulus,

Y = FAΔll{{{F \over A}} \over {{{\Delta l} \over l}}} = TAΔll{{{T \over A}} \over {{{\Delta l} \over l}}}

[As here F = T]

⇒\Rightarrow YΔll{Y{{\Delta l} \over l}} = TA{{T \over A}} = v2μA{{{{v^2}\mu } \over A}}

⇒\Rightarrow Δ\Delta l = v2μlAY{{{{v^2}\mu l} \over {AY}}}

= 90×90×60×10−360×10−2×60×10−21×10−6×16×1011{{90 \times 90 \times {{60 \times {{10}^{ - 3}}} \over {60 \times {{10}^{ - 2}}}} \times 60 \times {{10}^{ - 2}}} \over {1 \times {{10}^{ - 6}} \times 16 \times {{10}^{11}}}}

= 3 ×\times 10-5 m

= 0.03 mm

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