Young's moduli of two wires A and B are in the ratio 7:4 wire. 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 closed to:

 

  • Option 1)

    1.5 mm

  • Option 2)

    1.9 mm

  • Option 3)

    1.7 mm

  • Option 4)

    1.3 mm

 

Answers (1)

Y =\frac{F\l }{\pi r^{2}\Delta \l }

\frac{Y_{A}}{Y _{B}}=\frac{F\l_{A}}{\pi r_{A}^{2}\Delta \l_{A}} \times \frac{\pi r_{B}^{2}\Delta \l_{B}}{F\l_{B}}

\frac{7}{4}=\frac{2}{\left ( r_{A} \right )^{2}} \times \frac{2^{2}}{1.5}

\Rightarrow r_{A}^{2}=\frac{4 \times 2 \times 2^{2}}{1.5 \times 7}

\Rightarrow r_{A}=1.7 mm


Option 1)

1.5 mm

Option 2)

1.9 mm

Option 3)

1.7 mm

Option 4)

1.3 mm

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