Question

Three particles A, B and C move in a circle in anticlockwise direction with speeds 1 $m{s}^{-1},2.5m{s}^{-1}and2m{s}^{-1}$ respectively. The initial positions of A, B and C are as shown in figure. The ratio of distance travelled by B and C by the instant A, B and C meet for the first time is

• A. 3:2
• B. 5:4
• C. 3:5
• D. data insufficient

Answer 1

The correct option is B 5:4

Let the particles meet at point P after time t.

Thus using ${\theta }^{\prime }=wt$ where $w=\frac{v}{r}$

For A: $\theta =\frac{1}{r}t$ ..................(1)

For B: $\theta +\frac{\pi }{2}=\frac{2.5}{r}t$ ................(2)

For C: $\theta +\pi =\frac{2}{r}t$ .....................(3)

Dividing (2) by (3), we get $\theta =-3\pi$

Thus, distance moved by B, ${\theta }_B=-3\pi +\frac{\pi }{2}=-2.5\pi$

Distance moved by C, ${\theta }_C=-3\pi +\pi =-2\pi$

${\theta }_B:{\theta }_C=5:4$