Question

Two particle $P$ and $Q$ are at a distance of $10m$ at any moment. Velocities of $P$ and $Q$ are $8m/s$ respectively. The make an angle of ${30}^o$ with line $PQ$ as shown in fig. Angular velocity of $P$ with respect to $Q$ will be:

• A. $0rad/s$
• B. $0.1rad/s$
• C. $0.4rad/s$
• D. $0.7rad/s$

Answer 1

The correct option is D $0.7rad/s$

Distance between P and Q $=10m$

Velocity of P $=8m/s$

Velocity of Q $=6m/s$

Angular velocity of P with respect to Q will be

$\omega =\frac{8\sin 30+6\sin 30}{10}$

$\omega =\frac{8\times \frac{1}{2}+6\times \frac{1}{2}}{10}$

$\omega =\frac{7}{10}=0.7rad/s$