STD 11 - 6. system of particles and rotational motion — NEET STD 11 Science — Question

When both move in opposite direction

$\theta_{1}=w t$

$\theta_{2}=5 w t$

They meet each other when $\theta_{2}+\theta_{1}=2 \pi$

$\therefore 5 w t+w t=2 \pi$

$\therefore w t=\frac{\pi}{3}=60^{\circ}$

le. the bodies cross each other at points subtending an angle of $60^{\circ}$ if their angular velocities are directed opposite to each other.

case $2$

When both move in same direction $\theta_{1}=w t$

$\theta_{2}=5 w t$

They meet each other when $\theta_{2}-\theta_{1}=2 \pi$

$\therefore 5 w t-w t=2 \pi$

$\therefore w t=\frac{\pi}{2}=90^{\circ}$

i.e. the bodies cross each other at points subtending an angle of $90^{\circ}$ if their angular velocities are similar.

Now, when opposity directed, beat frequency$:$

$=\boldsymbol{n}_{2}-\boldsymbol{n}_{1}$

$=\frac{5 w}{2 \pi}-\left(\frac{-w}{2 \pi}\right)$

$=\frac{3 w}{\pi}$

$\therefore T=\frac{\pi}{3 w}$