Three point particles P, Q, R move in a circl | vedclass

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(B) Let the initial angular positions be $	heta_P(0) = \pi$,$	heta_Q(0) = \pi/2$,and $	heta_R(0) = 0$ (taking $R$ at the positive $x$-axis).The ang

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(B) Let the initial angular positions be $	heta_P(0) = \pi$,$	heta_Q(0) = \pi/2$,and $	heta_R(0) = 0$ (taking $R$ at the positive $x$-axis).The angular positions at time $t$ are given by $	heta(t) = 	heta(0) + \omega t$.$	heta_P(t) = \pi + 5\pi t$$	heta_Q(t) = \pi/2 + 2\pi t$Particles $P$ and $Q$ meet when $	heta_P(t) = 	heta_Q(t) + 2n\pi$,where $n$ is an integer.$\pi + 5\pi t = \pi/2 + 2\pi t + 2n\pi$$3\pi t = 2n\pi - \pi/2$$3t = 2n - 0.5$$t = (2n - 0.5) / 3$For $0 \le t \le 1$:$0 \le (2n - 0.5) / 3 \le 1$$0 \le 2n - 0.5 \le 3$$0.5 \le 2n \le 3.5$$0.25 \le n \le 1.75$Since $n$ must be an integer,$n = 1$.Thus,they meet only once at $t = (2(1) - 0.5) / 3 = 1.5 / 3 = 0.5 	ext{ s}$.

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