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

(C) $\omega\left(R_{2}-R_{1}\right) \hat{i}$

(A) $\omega\left(R_{1}+R_{2}\right) \hat{i}$

(B) $-\omega\left(R_{1}+R_{2}\right) \hat{i}$

(D) $\omega\left(R_{1}-R_{2}\right) \hat{i}$

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Kinematics

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

V_{A} - V_{B}

t = \frac{π}{2 ω}

is given by :

(A) $ω (R_{1} + R_{2}) \hat{i}$
(B) $- ω (R_{1} + R_{2}) \hat{i}$
(C) $ω (R_{2} - R_{1}) \hat{i}$ ✓ Correct
(D) $ω (R_{1} - R_{2}) \hat{i}$

Answer: (C)

Solution

After a time

t = \frac{π}{2 ω}

each particle has turned through

ω t = \frac{π}{2}

, a quarter circle. Both then sit on the positive

y

-axis moving in the

- x

direction, with

v_{A} = - ω R_{1} \hat{i}

and

v_{B} = - ω R_{2} \hat{i}

. The relative velocity is

v_{A} - v_{B} = - ω R_{1} \hat{i} + ω R_{2} \hat{i} = ω (R_{2} - R_{1}) \hat{i}

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Kinematics →

More JEE Main questions on Kinematics

A projectile is thrown upward at an angle $6 0^{\circ}$ with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is $4 5^{\circ}$ with the horizontal. The initial speed of the projectile is ______ m/s.
JEE Main 2026View solution →
A river of width 200 m is flowing from west to east with a speed of $18 km / h$ . A boat, moving with speed of $36 km / h$ in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for thi …
JEE Main 2026View solution →
An object is projected with kinetic energy K from a point A at an angle $6 0^{\circ}$ with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :
JEE Main 2026View solution →
A block is sliding down on an inclined plane of slope $θ$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$ . The distance $(S)$ travelled by the block before its velocity become zero, …
JEE Main 2026View solution →
A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 m / s^{2}$ . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is …
JEE Main 2026View solution →
A bead $P$ sliding on a frictionless semi-circular string $(A C B)$ and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$ . Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ …
JEE Main 2026View solution →