Question

Two equal mass objects are moving in a circular path with constant speed as shown in the figure. The collision is elastic everytime. They meet at $A$ again on $n^{th}$ collision, find the value of $n?$

[Assume, collisions are elastic in nature]

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

For elastic collision of equal mass objects, the velocities are interchanged.

$\Rightarrow$Object with speed $v$ and $3v$ will cover $\frac{1}{4}\text{th}$ and $\frac{3}{4}\text{th}$ of the total distance, respectively.

Therefore following figures represent the velocity of masses after collision:-

First collision:
Second collision:


Third collision:


Fourth collision will be at A, when they meet at A. So, the exchange of velocities after they collide at A is shown as:


Therefore, the masses meet at A after $4$ collisions from beginning.