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Q.

Two particles P and Q start from the origin and execute simple harmonic motion along x-axis with the same amplitude and time periods 3s and 6s. respectively. The ratio of the velocities of P and Q when they meet is

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a

3:2

b

2:3

c

1: 2

d

2:1

answer is B.

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Detailed Solution

Since the particles start from x=0 and have the same amplitude but different time periods, they will meet again at x=0 where their velocities are maximum equal to $a ω_{1}$ and $a ω_{2}$ , i.e.
$\frac{v_{1}}{v_{2}} = \frac{ω_{1}}{ω_{2}} = \frac{2 π}{T_{1}} \times \frac{T_{2}}{2 π} = \frac{T_{2}}{T_{1}} = \frac{6}{3} = 2$

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Two particles P and Q start from the origin and execute simple harmonic motion along x-axis with the same amplitude and time periods 3s and 6s. respectively. The ratio of the velocities of P and Q when they meet is