Q 11-08-081JEE MainJEE Main 2021 (24 Feb, Shift 1)Medium
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.
Answer: (C) $K = \frac{Y\eta}{9\eta-3Y}\ \text{N m}^{-2}$
The standard relation is $Y = \dfrac{9K\eta}{3K+\eta}$. Rearranging:
$$3KY + Y\eta = 9K\eta \;\Rightarrow\; K(9\eta - 3Y) = Y\eta \;\Rightarrow\; K = \frac{Y\eta}{9\eta - 3Y}$$
The other options do not follow (for example, solving for $\eta$ gives $\eta = \dfrac{3YK}{9K - Y}$, not $9K + Y$).
Solution by Sreeraj P, M.Sc Physics