Sankalp NEET Full Test-4 Question-23 Solution

Question: 23: The displacement-time graphs of two moving particles make angles of 30^{\circ} and 45^{\circ} with the x-axis as shown in the figure. The ratio of their respective velocity is

(1) 1: 2

(2) 1: \sqrt{3}

(3) \sqrt{3}: 1

(4) 1: 1

Answer: Option (2)

Explanation:

In a displacement-time graph, the slope of the graph gives the velocity of the particle.

If a straight line makes an angle \theta with the time axis, then its slope is given by

\text{velocity} = \tan \theta

For the first particle, the graph makes an angle of 30^{\circ} with the time axis.

v_1 = \tan 30^{\circ} = \frac{1}{\sqrt{3}}

For the second particle, the graph makes an angle of 45^{\circ} with the time axis.

v_2 = \tan 45^{\circ} = 1

The ratio of their velocities is

v_1 : v_2 = \frac{1}{\sqrt{3}} : 1

Multiplying both terms by \sqrt{3}, we get

v_1 : v_2 = 1 : \sqrt{3}

Hence, the correct answer is Option (2).