Question

q.19. the graph shows the relationship between mass and volume for different substances. which of the substances has the greatest density? a) substance a b) substance b c) substance c d) substance d

Explanation:

Density is calculated by the formula $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume. For a mass - volume graph, the slope of the line representing the relationship between mass and volume is equal to the density (since $
ho=\frac{\Delta m}{\Delta V}$). A steeper slope indicates a greater density.

Step 1: Analyze the slope concept

The slope of a line in a mass - volume graph is given by $slope=\frac{\text{Change in Mass}}{\text{Change in Volume}}$, and this is equal to the density of the substance. So, we need to compare the slopes of the lines for Substance A, B, C, and D.

Step 2: Compare the slopes

Looking at the graph, the line for Substance A has the steepest slope among the lines for Substance A, B, C, and D. This is because for a given change in volume, the change in mass for Substance A is the largest (or for a given change in mass, the change in volume is the smallest) compared to the other substances. Since slope = density, a steeper slope means a greater density.

Answer:

a) Substance A