Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed Ω. At t = 0, their positions and direction of motion are shown in the figure: The relative velocity vec∈A - vec∈B at t = (π/2 Ω) is given by :

Question

Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed Ω. At t = 0, their positions and direction of motion are shown in the figure: The relative velocity vec∈A - vec∈B at t = (π/2 Ω) is given by : (A) -ω(R1 + R2) hati (B) ω(R1 + R2) hati (C) ω(R1 - R2) hati (D) ω(R2 - R1) hati

Tardigrade Admin · Accepted Answer

θ = ω t = ω (π/2ω) = (π/2) vec VA - vec VS = ω R1 (- hati) - ω R2(-i)

Q. Two particles $A, B$ are moving on two concentric circles of radii $R_{1}$ and $R_{2}$ with equal angular speed $Ω$ . At $t = 0$ , their positions and direction of motion are shown in the figure : The relative velocity $\in_{A} - \in_{B} a t t = \frac{π}{2Ω}$ is given by :

$- ω (R_{1} + R_{2}) \hat{i}$

$ω (R_{1} + R_{2}) \hat{i}$

$ω (R_{1} - R_{2}) \hat{i}$

$ω (R_{2} - R_{1}) \hat{i}$

$θ = ω t = ω \frac{π}{2 ω} = \frac{π}{2}$
$V_{A} - V_{S} = ω R_{1} (- \hat{i}) - ω R_{2} (- i)$

Q. Two particles A,B are moving on two concentric circles of radii R1​ and R2​ with equal angular speed Ω. At t=0, their positions and direction of motion are shown in the figure : The relative velocity ∈​A​−∈​B​att=2Ωπ​ is given by :

−ω(R1​+R2​)i^

ω(R1​+R2​)i^

ω(R1​−R2​)i^

ω(R2​−R1​)i^