Rotational Motion Question 188
Question: A and B are moving in 2 circular orbits with angular velocity 2$\omega $ and $\omega $ respectively. Their positions are as shown at $t=0$ . Find the time when they will meet for the first time.
Options:
A) $\frac{\pi }{2\omega }$
B) $\frac{3\pi }{2\omega }$
C) $\frac{\pi }{\omega }$
D) they will never meet
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Case 1: When they rotate in same sense
$2m\pi =2\omega t$
$\frac{3\pi }{2}+2n\pi =\omega t;2m\pi =2\left( \frac{3\pi }{2}+2n\pi\right)$
$2m=3+4n;m=\frac{3}{2}+2n\Rightarrow m-2n=\frac{3}{2}$
Not possible for m and n being integer.
Case 2: When they rotate in opposite sense
$\frac{\pi }{2}+2n\pi =\omega t;2m\pi =2\left( \frac{\pi }{2}+2n\pi\right)$
$2m\pi =\pi +4n\pi ;2m-4n=1$
Not possible for m and n integer.
