MCQ
The displacement-time graph for two particles $A$ and $B$ are straight lines inclined at angles of ${30^o}$ and ${60^o}$ with the time axis. The ratio of velocities of ${V_A}:{V_B}$ is
- A$1:2$
- B$1:\sqrt 3 $
- C$\sqrt 3 :1$
- ✓$1:3$
✓
Answer
Correct option: D.
$1:3$
d
(d)$\frac{{{v_A}}}{{{v_B}}} = \frac{{\tan {\theta _A}}}{{\tan {\theta _B}}}$ $ = \frac{{\tan 30^\circ }}{{\tan 60^\circ }}$$ = \frac{{1/\sqrt 3 }}{{\sqrt 3 }} = \frac{1}{3}$
(d)$\frac{{{v_A}}}{{{v_B}}} = \frac{{\tan {\theta _A}}}{{\tan {\theta _B}}}$ $ = \frac{{\tan 30^\circ }}{{\tan 60^\circ }}$$ = \frac{{1/\sqrt 3 }}{{\sqrt 3 }} = \frac{1}{3}$
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