A student carried out an experiment to determine the Young modulus of copper. She added a mass $$\(m\)$$ to the free end of a sample of copper in the form of a long thin wire and the corresponding extension $$\(\Delta x\)$$ was measured. This was repeated for increasing masses. The student repeated the measurement of the diameter of the wire at different positions and orientations of the wire. She obtained the following results. (i) Determine the cross-sectional area of the sample of wire used. (3) Cross-sectional area $$\(=\)$$ (ii) The student plotted a graph of $$\(m\)$$ against $$\(\Delta x\)$$. She measured the gradient and obtained a value of $$\(195 \mathrm{~kg} \mathrm{~m}^{-1}\)$$. Determine the Young modulus of the copper. length of sample of copper used $$\(=3.50 \mathrm{~m}\)$$ (3) Young modulus $$\(=\)$$ (iii) The experiment was repeated by another student, using a $$\(2.00 \mathrm{~m}\)$$ length of the copper wire. Suggest how the values obtained for the gradient and hence the Young modulus will differ between the students. (2)

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