JEE PYQ: Properties Of Matter Question 3
Question 3 - 2021 (24 Feb 2021 Shift 1)
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.
(1) $K = \frac{Y\eta}{9\eta - 3Y}$ N/m$^2$
(2) $\eta = \frac{3YK}{9K - Y}$ N/m$^2$
(3) $Y = \frac{9K\eta}{3K - \eta}$ N/m$^2$
(4) $Y = \frac{9K\eta}{2\eta + 3K}$ N/m$^2$
Show Answer
Answer: (1)
Solution
$Y = 3K(1 - 2\sigma) \Rightarrow \sigma = \frac{1}{2}\left(1 - \frac{Y}{3K}\right)$ …(1)
$Y = 2\eta(1 + \sigma) \Rightarrow \sigma = \frac{Y}{2\eta} - 1$ …(2)
Comparing (1) and (2): $\frac{Y}{2\eta} - 1 = \frac{1}{2}\left(1 - \frac{Y}{3K}\right) \Rightarrow K = \frac{Y\eta}{9\eta - 3Y}$
BETA
