Question

Two particles, P and Q are initially at two ends of a circular arc which subtends an angle 120${}^o$ at the arc-center. The radius of the arc is r. The particles P and Q are moving along the arc towards each other with constant tangential velocities of $V_P$ and $V_Q$ respectively. The distance travelled by the particle P when it meets the particle Q is

• A. $\frac{2\pi }{3}\frac{r(V_P+V_Q)}{V_P}$
• B. $\frac{2\pi }{3}\frac{r(V_P+V_Q)}{V_Q}$
• C. $\frac{2\pi }{3}\frac{r{V}_P}{(V_P+V_Q)}$
• D. $\frac{2\pi }{3}\frac{r{V}_Q}{(V_P+V_Q)}$

Answer 1

The correct option is C $\frac{2\pi }{3}\frac{r{V}_P}{(V_P+V_Q)}$


$(\frac{V_P}{r}+\frac{V_Q}{r})t=120\times \frac{\pi }{180}$

$t=\frac{120\pi r}{180(V_P+V_Q)}$

$\text{Distance traveled by}P=r.\frac{V_P}{r}.t$

$=V_P.t$

$=\frac{120\pi r{V}_P}{180(V_P+V_Q)}$

$=\frac{2\pi r{V}_P}{3(V_P+V_Q)}$