Question

Two particles A and B are moving with constant velocities $v_1=\hat{j}$ and $v_2=2\hat{i}$ respectively A is at co-ordinates $(0,0)$ and B is at $(-4,0)$.the angular velocity of B with respect to A at $t=2s$ is (all physical quantities are in SI units)

• A. $\frac{1}{2}rad/s$
• B. $2rad/s$
• C. $4rad/s$
• D. $1rad/s$

Answer 1

The correct option is D $1rad/s$

After $2\sec$ the particle A will be at $(0,2)$ and co-ordinate of B will be $(0,0)$

So,the angular velocity of $B$ w.r.t $A$ will be taking $A$ taking $A$ as centre of circle perpendicular and $B$ the point.So, the distance between the velocities of both particles is $r=2$
So, $V=Wr$
velocity of B w.r.t of A is $\overrightarrow{V}=2\hat{i}-0$
$w=\frac{v}{r}$
$|w|=1rad/sec$