# Inelastic Sphere Collision!

**Classical Mechanics**Level 5

Let angular velocity and Velocity of centre of sphere after

**immediately**after the collision is in 'x' and 'y' direction will be expressed as :

\[ \begin{align} { v }_{ x } &= \cfrac { a }{ b } \times \mu { v }_{ o }\\ { v }_{ y }&= \cfrac { c }{ d } \times { v }_{ o }\\ { { \omega } }^{ " }&= \cfrac { (\alpha -\beta \times \mu ) }{ \gamma R } \times { v }_{ o } \end{align} \]

Then find the value of :

\[a + b + c + d + \alpha +\beta +\gamma. \]

**Details and assumptions**

\(\bullet \) gcd (a , b ) = 1

\(\bullet \) gcd (c,d ) = 1

\(\bullet \) gcd (\(\alpha \) , \(\beta \) ) = 1

\(\bullet \) gcd ( \(\gamma \) , \(\beta \) ) = 1

\(\bullet \) All are positive integers.

\(\bullet \) Take clockwise direction as positive.

###### This is part of my set Deepanshu's Mechanics Blasts

Source : My Friend give me as challange , Unfortunately He is not on Brilliant .