Question

Six particles situated at the corners of a regular hexagon of side $a$ move at a constant speed $v$. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other .

• A. $\frac{2a}{3v}$
• B. $\frac{v}{a}$
• C. $\frac{2a}{v}$
• D. $\frac{a}{3v}$

Answer 1

The correct option is C $\frac{2a}{v}$

Concentrate on two particles adjacent to each other. The displacement of one particle with respect to other $=a$

Now, the relative velocity of one particle with respect to other towards it is:

$v_r=v-vcos{60}^{\circ }$$=v-\frac{v}{2}=\frac{v}{2}$

Relative velocity $=$ Total displacement/Time taken

$⟹\frac{v}{2}=\frac{a}{t}$

$⟹t=\frac{2a}{v}$