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Mechanical Properties of Solids question bank (Physics)

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Q1.

$A$ 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:

(A)

$\frac{MgY}{\pi r \sigma}$

(B)

$\frac{Mg \sigma}{\pi rY}$

(C)

$\frac{\sigma \pi r}{MgY}$

(D)

$\frac{Mgr}{\sigma \pi Y}$

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Q2.

$A$ wire of Young's modulus $1.6 \times 10^{12} \,N/m^{2}$ is stretched by a force so as to produce a strain of $2 \times 10^{-4}$. The energy density of the wire is

(A)

$3.2 \times 10^{4} \,J/m^{3}$

(B)

$3.2 \times 10^{8} \,J/m^{3}$

(C)

$1.6 \times 10^{3} \,J/m^{3}$

(D)

$6.4 \times 10^{3} \,J/m^{3}$

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