COMEDK · Physics · 10. Mechanical Properties of Solids
If the ratio of lengths, radii and Young's Moduli of steel and brass wires in the figure are \(\mathrm{a}, \mathrm{b}\) and \(\mathrm{c}\) respectively, then the corresponding ratio of increase in their lengths would be
- A \(\dfrac{3 a}{2 b^2 c}\)
- B \(\dfrac{2 \mathrm{ab}^2}{c}\)
- C \(\dfrac{2 a}{3 b^2 c}\)
- D \(\dfrac{a}{3 b^2 c}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{2 a}{3 b^2 c}\)
Step-by-step Solution
Detailed explanation
Let \(L_s, r_s, Y_s\) be the length, radius, and Young's modulus of the steel wire, and \(L_b, r_b, Y_b\) be those of the brass wire. Given ratios are \(\dfrac{L_s}{L_b} = a\), \(\dfrac{r_s}{r_b} = b\), and \(\dfrac{Y_s}{Y_b} = c\). The tension in the steel wire is \(T_s = 2Mg\)…
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