# Geometry + Mechanics = Geonics

**Classical Mechanics**Level 4

**d**, Initially

**n**identical particles each of mass

**m**are placed rest at the vertices of the polygon. Then at time

**t=0**they start moving with constant speed \({ v }_{ o }\) each such that they always moves in direction towards the adjacent particle. Let the total time taken by particles when they meets is

**T**.

If circum-radius of the Regular polygon is **R** and it's in-radius is **r** .

If the value of

\[\frac { r }{ R } \quad =\quad \sqrt { 1-\quad (\cfrac { x }{ y } \times \frac { d }{ { v }_{ o }T } ) }\].

Then Find value of \[1729\quad \times \quad \cfrac { x }{ y } \quad \]

**Details and assumptions**

\(\bullet \) **x** and **y** are positive co-prime integers.