Question

The displacement time graph for two particles $A$ and $B$ are straight lines inclined at angles of ${30}^{\circ }$ and ${60}^{\circ }$ respectively with the time axis. The ratio $V_A:V_B$ is

• A. $1:2$
• B. $1:\sqrt{3}$
• C. $1:3$
• D. $3:1$

Answer 1

The correct option is C $1:3$

The displacement time graph for $A$ and $B$:

We know that, velocity is given by the slope of line in displacement time graph.
$V_A=\tan {\theta }_1$, where ${\theta }_1$ is the angle made by $A$ with X-axis.
Similarly, $V_B=\tan {\theta }_2$
Here, ${\theta }_1={30}^{\circ }$ and ${\theta }_2={60}^{\circ }$
$\therefore \frac{V_A}{V_B}=\frac{\tan {\theta }_1}{\tan {\theta }_2}=\frac{\tan 30}{\tan 60}=\frac{1}{\sqrt{3}\times \sqrt{3}}\Rightarrow \frac{V_A}{V_B}=\frac{1}{3}$