Read the following two statements below carefully and state,with reasons,if it is true or false.
$(a)$ The Young's modulus of rubber is greater than that of steel;
$(b)$ The stretching of a coil is determined by its shear modulus.
$(a)$ The Young's modulus of rubber is greater than that of steel;
$(b)$ The stretching of a coil is determined by its shear modulus.
(A) False. For a given stress,the strain produced in rubber is much larger than the strain produced in steel. Since Young's modulus $Y = \frac{\text{Stress}}{\text{Strain}}$,and $Y$ is inversely proportional to strain for a constant stress,the Young's modulus of rubber is less than that of steel.
$(b)$ True. The stretching of a coil involves a change in the shape of the wire forming the coil without changing its length significantly. This deformation is characterized by the shear modulus of the material.
$(b)$ True. The stretching of a coil involves a change in the shape of the wire forming the coil without changing its length significantly. This deformation is characterized by the shear modulus of the material.
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| Column $I$ | Column $II$ |
|---|---|
| $A$. Hooke's law | $1$. Tangential strain |
| $B$. Shearing strain | $2$. Temporary loss of elastic property |
| $C$. Bulk strain | $3$. Elastic limit |
| $D$. Elastic fatigue | $4$. $3$ times the linear strain |
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