Question

Three point particles $P,Q,R$ move in a circle of radius ${}^{\prime }{r}^{\prime }$ with different but constant speeds. They start moving at $t=0$ from their initial positions as shown in the figure. The angular velocities (in rad/sec) of $P,Q$ and $R$ are $5\pi ,2\pi \&3\pi$ respectively, in the same sense. The time interval after which they all meet is

• A. $\frac{2}{3}sec$
• B. $\frac{1}{6}sec$
• C. $\frac{1}{2}sec$
• D. $\frac{3}{2}sec$

Answer 1

The correct option is D $\frac{3}{2}sec$

relative angular speed of P and Q particles, $5\pi -2\pi =3\pi$

They will meet at

$t_1=\frac{2\pi +\pi /2}{3\pi }=\frac{2.5}{3}s$,

$t_2=\frac{4\pi +\pi /2}{3\pi }=\frac{4.5}{3}=\frac{3}{2}s$,

$t_3=\frac{6\pi +\pi /2}{3\pi }=\frac{6.5}{3}s$ ,

Relative angular speed of P and R particles, $5\pi -3\pi =2\pi$

They will meet at

$t_4=\frac{2\pi +\pi }{2\pi }=\frac{3}{2}s$,

$t_5=\frac{4\pi +\pi }{2\pi }=\frac{5}{2}s$

$t_6=\frac{6\pi +\pi }{2\pi }=\frac{7}{2}s$ ,

All particle will meet at time,$T=\frac{3}{2}s$