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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the angular positions at $t=0$ be $	heta_P(0) = \pi$, $	heta_Q(0) = \pi/2$, and $	heta_R(0) = 0$.The angular positions at time $t$ are:$	h

Vedclass · Accepted Answer

$1/2 \, s$

Vedclass · Answer

(C) Let the angular positions at $t=0$ be $	heta_P(0) = \pi$, $	heta_Q(0) = \pi/2$, and $	heta_R(0) = 0$.The angular positions at time $t$ are:$	heta_P(t) = 5\pi t + \pi$$	heta_Q(t) = 2\pi t + \pi/2$$	heta_R(t) = 3\pi t + 0$For particles $P$ and $Q$ to be at the same position: $	heta_P(t) - 	heta_Q(t) = 2n\pi$ (where $n$ is an integer).$3\pi t + \pi/2 = 2n\pi \implies 3t = 2n - 1/2 \implies t = (4n-1)/6$.For $n=1, t = 3/6 = 1/2 \, s$. For $n=2, t = 7/6 \, s$. For $n=3, t = 11/6 \, s$.For particles $Q$ and $R$ to be at the same position: $	heta_Q(t) - 	heta_R(t) = 2m\pi$.$-\pi t + \pi/2 = 2m\pi \implies t = 1/2 - 2m$.For $m=0, t = 1/2 \, s$. For $m=-1, t = 2.5 \, s$.Comparing the times, they all meet at $t = 1/2 \, s$.

Similar Questions

Two bodies of masses $m$ and $3m$ are rotating in horizontal circles of radii $r$ and $\frac{r}{3}$ respectively. The tangential speed of the body of mass $m$ is $n$ times that of the heavier body. If the centripetal force is the same for both,the value of $n$ is:

$A$ boy is moving with a constant speed $v$ on a small trolley towards a distant circle as shown in the figure. $A$ point mass is moving on the circle with a constant speed $v$. What is the frequency of change in the magnitude of the relative velocity of the point mass,as observed by the boy?

$A$ particle is moving in the $xy$-plane in a circular path with its center at the origin. If at an instant the position of the particle is given by $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$,then the velocity of the particle is along .......

The diameter of a car wheel is $60 \ cm$. How many radians of angular displacement will the wheel have undergone while the car travels a distance of $1.2 \ km$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module