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 [2022]

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Solution

Q.
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 [2022]

1 $\sqrt{3} : 1$

2 $1 : 1$

3 $1 : 2$

4 $1 : \sqrt{3}$

Ans.
(4)

The slope of displacement time graph gives velocity

$so, v_{1} = \tan 30 °; v_{2} = \tan 45 °$

$so, \frac{v_{1}}{v_{2}} = \frac{\tan 30 °}{\tan 45 °} = \frac{1}{\sqrt{3} \times 1} = 1 : \sqrt{3}$

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