JEE Mains · Physics · STD 11- 8. mechanical properties of solids
Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object:
- A \(\sigma=\frac{3 K -2 \eta}{6 K +2 \eta}\)
- B \(\sigma=\frac{6 K +2 \eta}{3 K -2 \eta}\)
- C \(\sigma=\frac{3 K+2 \eta}{6 K+2 \eta}\)
- D \(\sigma=\frac{6 K -2 \eta}{3 K -2 \eta}\)
Answer & Solution
Correct Answer
(A) \(\sigma=\frac{3 K -2 \eta}{6 K +2 \eta}\)
Step-by-step Solution
Detailed explanation
\(Y =3 \eta(1+\sigma)\) \(Y =3 K (1-\sigma)\) \(\Rightarrow 2 \eta(1+\sigma)=3 K (1-2 \sigma)\) \(\Rightarrow \sigma=\left(\frac{3 K -2 \eta}{6 K +2 \eta}\right)\)
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