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(C) The correct matches are as follows:$A$. Hooke's law: Within the elastic limit,stress is directly proportional to strain. Thus,$A-3$.$B$. Shearing

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$A-3, B-1, C-4, D-2$

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(C) The correct matches are as follows:$A$. Hooke's law: Within the elastic limit,stress is directly proportional to strain. Thus,$A-3$.$B$. Shearing strain: It is defined as the angle in radians through which a plane perpendicular to the fixed surface of a cubical body gets turned under the effect of a tangential force. It is also known as tangential strain. Thus,$B-1$.$C$. Bulk strain: For a solid,the volumetric strain (bulk strain) is equal to $3$ times the linear strain. Thus,$C-4$.$D$. Elastic fatigue: The temporary loss of elastic properties due to the action of repeated alternating deforming forces is called elastic fatigue. Thus,$D-2$.Therefore,the correct matching is $A-3, B-1, C-4, D-2$,which corresponds to option $C$.

Match the following:
| 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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Match the following:| 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 |