TS EAMCET · Physics · Mechanical Properties of Solids
A steel rod with a circular cross-section of diameter 1 cm and another steel rod with a square cross-section of side 1 cm have equal mass. If the two rods are subjected to same tension, the ratio of the elongations of the two rods is
- A \(\frac{1}{\pi^2}\)
- B \(\frac{2}{\pi^2}\)
- C \(\frac{4}{\pi^2}\)
- D \(\frac{16}{\pi^2}\)
Answer & Solution
Correct Answer
(D) \(\frac{16}{\pi^2}\)
Step-by-step Solution
Detailed explanation
\( A_c = \pi (d_c/2)^2 = \pi (1/2)^2 = \frac{\pi}{4} \) \( A_s = a_s^2 = 1^2 = 1 \) \( \Delta L = \frac{FL}{AE} \) \( m_c = m_s \implies \rho A_c L_c = \rho A_s L_s \implies A_c L_c = A_s L_s \implies \frac{L_c}{L_s} = \frac{A_s}{A_c} \)…
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