Q105 / 200 · NEET 2022 (Phase 1) · Physics

The displacement-time graphs of two moving particles make angles of $30 °$ and $45 °$ with the $x$ -axis as shown in the figure. The ratio of their respective velocity is:

A
$1 : 1$
B
$1 : 2$
Correct answer
C
$1 : \sqrt{3}$
D
$\sqrt{3} : 1$

Solution

Slope of displacement-time graph is velocity.

\frac{v_{1}}{v_{2}} = \frac{\tan (θ_{1})}{\tan (θ_{2})} = \frac{\tan (30 °)}{\tan (45 °)} = \frac{1}{\sqrt{3}}

\Rightarrow v_{1} : v_{2} = 1 : \sqrt{3}

Hence, the correct answer is option: 'C'.

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