question_answer

The displacement-time graph for two particles A and B are straight line inclined at angles of \[30{}^\circ \] and \[60{}^\circ \] with the time axis. The ratio of velocities, \[{{v}_{A}}:{{v}_{B}}\] is

A) 1 : 2                 

B) 1 :\[\sqrt{3}\]

C) \[\sqrt{3}\] : 1                           

D) 1 : 3

Correct Answer: D

Solution :

[d] Slope (= tan 9), of displacement-time graph shows velocity.

\[\frac{{{v}_{A}}}{{{v}_{B}}}=\frac{\tan {{\theta }_{A}}}{\tan {{\theta }_{B}}}=\frac{\tan {{30}^{\operatorname{o}}}}{\tan {{60}^{\operatorname{o}}}}=\frac{1/\sqrt{3}}{\sqrt{3}}=\frac{1}{3}=1:3\]