Question 351: Properties of Matter

Question

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

Accepted Answer

From formula,
Increase in length $$\Delta L = {{FL} \over {AY}} = {{4FL} \over {\pi {D^2}Y}}$$
$${{\Delta {L_S}} \over {\Delta {L_C}}} = {{{F_S}} \over {{F_C}}}{\left( {{{{D_C}} \over {{D_S}}}} ight)^2}{{{Y_C}} \over {{Y_S}}}{{{L_S}} \over {{L_C}}}$$
$$ = {7 \over 5} 	imes {\left( {{1 \over p}} ight)^2}\left( {{1 \over s}} ight)q = {{7q} \over {\left( {5s{p^2}} ight)}}$$

Answer

$$\left( {{{5q} \over {7s{p^2}}}} \right)$$

Answer

$$\left( {{{7q} \over {5s{p^2}}}} \right)$$

Answer

$$\left( {{{2q} \over {5sp}}} \right)$$

Answer

$$\left( {{{7q} \over {5sp}}} \right)$$

Properties of Matter

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

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