The density of 400cm ^3 of palm oil was 0.9gcm-3 before frying. If the density of the oil was 0.6gcm-3 after…

Analysis

To solve this problem, we must understand the relationship between mass, density, and volume. The key principle here is the Law of Conservation of Mass: since the problem states there is no loss of oil due to spilling, the mass of the palm oil remains constant before and after frying.

Concept

The formula for density ($\rho$) is:

Where:

• $\rho$ = density
• $m$ = mass
• $V$ = volume

Since mass ($m$) is constant, we can express it as $m = \rho \times V$. Therefore, the mass before frying must equal the mass after frying:

Step-by-Step Solution

1. Identify the given values: • Initial density ($\rho_1$) = $0.9 \, \text{g/cm}^3$ • Initial volume ($V_1$) = $400 \, \text{cm}^3$ • Final density ($\rho_2$) = $0.6 \, \text{g/cm}^3$ • Final volume ($V_2$) = ?

2. Calculate the mass of the oil: $$m = \rho_1 \times V_1$$ $$m = 0.9 \, \text{g/cm}^3 \times 400 \, \text{cm}^3 = 360 \, \text{g}$$

3. Calculate the new volume ($V_2$) using the final density: Since $m = \rho_2 \times V_2$: $$360 \, \text{g} = 0.6 \, \text{g/cm}^3 \times V_2$$ $$V_2 = \frac{360}{0.6}$$ $$V_2 = 600 \, \text{cm}^3$$

Conclusion

By equating the mass before and after the process, we find that the new volume of the oil is $600 \, \text{cm}^3$.

Exam Tip

Whenever you see a problem involving a change in state or condition where the substance itself is not lost (like this one), always look for the quantity that remains constant (in this case, mass). Setting the constant quantity equal on both sides of the equation is the fastest way to solve these types of JAMB physics problems!