Two  particles move on  a circular  path (one just  inside  and the other  just outside the circle) with  angular  velocities   ω and5ω starting  from the  same position .They  cross  each other

# Two  particles move on  a circular  path (one just  inside  and the other  just outside the circle) with  angular  velocities   $\omega \text{\hspace{0.17em}}and5\omega$ starting  from the  same position .They  cross  each other

1. A

At intervals of time $\frac{\pi }{4\omega }$ if  their  angular  velocities  are in the same  sense

2. B

At successive  points  on the  path  subtending  an angle  of at the center  if their angular  velocities   are opposite  directed

3. C

At  intervals  of  time $\frac{\pi }{3\omega }$if their  angular  velocities  are oppositely  directed

4. D

At successive  points  on the path  subtending  an angle  of $45°C$ at the center if  their  angular velocities are oppositely  directed

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### Solution:

${t}_{1}=\frac{2\pi }{6\omega }=\frac{\pi }{3\omega }⇒\left(C\right){\varphi }_{1}=\frac{\pi }{3\omega }x\omega =\frac{\pi }{3}⇒\left(B\right)$

${t}_{2}=\frac{2\pi }{4\omega }=\frac{\pi }{2\omega }⇒\left(A\right)$is false

${\varphi }_{2}=\frac{\pi }{2\omega }x\omega =\frac{\pi }{2}⇒\left(D\right)$ is false

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