Question

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

• A. $1:2$
• B. $2:1$
• C. $2:3$
• D. $3:2$

Answer 1

Answer: (B)

$2:1$

The particles will meet at the mean position when $P$ completes one oscillation and $Q$ completes half an oscillation

The angular velocity for first particle is ${\omega }_1=\frac{2\pi }{3}$.

The angular velocity for second particle is ${\omega }_2=\frac{2\pi }{6}=\frac{\pi }{3}$

So, the velocities at different points will be:

$v_1={\omega }_{1}A$ and $v_2={\omega }_{2}A$

So, $\frac{v_1}{v_2}=\frac{{\omega }_1}{{\omega }_2}$

$\frac{v_1}{v_2}=\frac{2\pi /3}{\pi /3}$

$\frac{v_1}{v_2}=2:1$