The Young's modulus of the material of a wire is $6 \times 10^{12} \ N/m^2$ and there is no transverse strain in it,then its modulus of rigidity will be

  • A
    $3 \times 10^{12} \ N/m^2$
  • B
    $2 \times 10^{12} \ N/m^2$
  • C
    $10^{12} \ N/m^2$
  • D
    None of the above

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$A$ wire of length $L$ and radius $r$ is loaded with a weight $Mg$. If $Y$ and $\sigma$ denote the Young's modulus and Poisson's ratio of the material of the wire respectively,then the decrease in the radius of the wire $(\Delta r)$ is given by:

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