Verified Solution • 2025–26 Session moderate

QJEEM19Ph5a3c: JEE Main 2019 Physics - Class 11 JEEM19Ph5a3c Solution: Young's moduli of two wires A and B are in the ratio 7 : 4.…

Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to :-

Multiple Choice Options

  • A 1.7 mm
  • B 1.9 mm
  • C 1.3 mm
  • D 1.5 mm

Step-by-Step Verified Solution

Given:

YAYB=74; LA=2m ;AA=πR2{{{Y_A}} \over {{Y_B}}} = {7 \over 4};\,{L_A} = 2m\,;{A_A} = \pi {R^2}

FA=Y(lL);LB=1.5m ;AB=π(2mm)2{F \over A} = Y\left( {{l \over L}} \right);{L_B} = 1.5m\,;{A_B} = \pi {(2mm)^2}

given F and ll are same ⇒\Rightarrow AYL{{AY} \over L} is same

AAYALA=ABYBLB{{{A_A}{Y_A}} \over {{L_A}}} = {{{A_B}{Y_B}} \over {{L_B}}}

⇒(πR2)(74YB)2=π(2 mm)2.YB1.5\Rightarrow {{\left( {\pi {R^2}} \right)\left( {{7 \over 4}{Y_B}} \right)} \over 2} = {{\pi {{(2\,mm)}^2}.{Y_B}} \over {1.5}}

R = 1.74 mm

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