An object is made of two equal parts by volume; one part has density $\rho_0$ and the other part has density $2\rho_0$. What is the average density of the object?
$3 ho_0$
$ rac{3}{2} ho_0$
$ ho_0$
$ rac{1}{2} ho_0$
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-2 – 2022
Let $\rho_1$ be the density of the first part and $\rho_2$ be the density of the second part.
Given: $\rho_1 = \rho_0$ and $\rho_2 = 2\rho_0$.
The mass of the first part is $m_1 = \rho_1 \times V_1 = \rho_0 \times (V/2)$.
The mass of the second part is $m_2 = \rho_2 \times V_2 = 2\rho_0 \times (V/2) = \rho_0 V$.
The total mass of the object is $M = m_1 + m_2 = \rho_0 (V/2) + \rho_0 V = \rho_0 V (\frac{1}{2} + 1) = \rho_0 V (\frac{3}{2})$.
The total volume of the object is $V_{\text{total}} = V_1 + V_2 = V/2 + V/2 = V$.
The average density of the object is $\rho_{\text{avg}} = \frac{M}{V_{\text{total}}} = \frac{\rho_0 V (3/2)}{V} = \frac{3}{2}\rho_0$.