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Question 2.[10 marksl (a) A commercial strain gauge consists of rubber tubing, filled with ultra-pure mercury. When stretched, the cross sectional area, A, decreases and the resistance increases due to the changes in the gauge area and length. The resting resistance is R, and the resting length is L, and an increase of AL in the length will lead to an increase in the resistance of Remembering that the volume of the mercury remains constant (ie., if L increases by AL, A will decrease by A4) and that Ro ,where p is the resistivity, show that:

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