JEE Mains · Physics · STD 11- 8. mechanical properties of solids
If \(Y, K\) and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
- A \(Y =\frac{9 K \eta}{3 K -\eta} N / m ^{2}\)
- B \(\eta=\frac{3 YK }{9 K + Y } N / m ^{2}\)
- C \(Y =\frac{9 K \eta}{2 \eta+3 K } N / m ^{2}\)
- D \(K =\frac{ Y\eta }{9 \eta-3 Y } N / m ^{2}\)
Answer & Solution
Correct Answer
(D) \(K =\frac{ Y\eta }{9 \eta-3 Y } N / m ^{2}\)
Step-by-step Solution
Detailed explanation
\(Y-\) Younge modulus, \(K\) - Bulk modulus, \(\eta\) - modulus of rigidity We know that \(y=3 k(1-2 \sigma)\) \(\sigma=\frac{1}{2}\left(1-\frac{ y }{3 k }\right)\) \(.........(i)\) \(y =2 \eta(1+\sigma)\) \(\sigma=\frac{y}{2 \eta}-1\) \(........(ii)\) From Eq.\((i)\) and Eq.…
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