Q122 / 180 · KCET 2011 · Physics
The displacement-time graph of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the $X$-axis. The ratio of their velocities is
- A$\sqrt{3}: 2$
- B$1: 1$
- C$1: 2$
- Correct answerD$1: \sqrt{3}$
Solution
By the definition, the slope of displacement-time graph is velocity.
i.e., $\quad v=\tan \theta$
$\therefore \quad \frac{v_{1}}{v_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$\frac{v_{1}}{v_{2}}=\frac{\tan 30^{\circ}}{\tan 45^{\circ}}$
$\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{3}}$
Hence, the correct answer is option: 'D'.