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Q.

If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is:

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a

$\frac{2 a^{2} c}{h}$

b

$\frac{3 c}{2 a b^{2}}$

c

$\frac{2 a c}{b^{2}}$

d

$\frac{3 a}{2 b^{2} c}$

answer is C.

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Detailed Solution

Given $\frac{L_{s}}{L_{b}} = a, \frac{r_{s}}{r_{b}} = b, \frac{y_{s}}{y_{b}} = c, \frac{Δ L_{s}}{Δ L_{b}}, \frac{e_{s}}{e_{b}} =____$

$Y = \frac{F L}{A e} \to e = \frac{F L}{A y}$

$e_{s} = \frac{3 M g L_{s}}{π r_{s}^{2} y_{s}} [∵ F_{s} = (M + 2 M) g]$

$e_{b} = \frac{2 M g L_{b}}{π r_{b}^{2} y_{b}} \to \frac{e_{s}}{e_{b}} = \frac{3 a}{2 b^{2} C}$

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If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is: