Question

Three particle A,B and C move in a circle in anticlockwise direction with speeds $1m{s}^{-1},2.5m{s}^{-1}$ and $2m{s}^{-1}$ respectively. The initial positions of A, B and C are as shown in the figure. The ratio of distance travelled by B and C at 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


When A, B and C meet for first time, let ${\theta }_A,{\theta }_B,{\theta }_C$ be their angular displacements in time $t$

Now,
${\theta }_A=w_{A}t=\frac{V_A\times t}{R}=\frac{t}{R}$
${\theta }_B=\frac{V_B\times t}{R}=\frac{5t}{2R}$
${\theta }_C=\frac{V_C\times t}{R}=\frac{2t}{R}$
Then, ratio of arc lengths i.e distance travelled by B and C is
$\frac{S_B}{S_C}=\frac{R{\theta }_B}{R{\theta }_C}=\frac{5}{4}$