# Save all ants from Monster Cube !

**Classical Mechanics**Level 5

A **solid** Cube of side Length **L** and Mass **M** is moving on horizontal **smooth** table with velocity \({ V }_{ o }\) . ( Side View is shown in figure )

An ridge ( Considered it as a Small stone ) is fixed at the corner of table.( Red coloured,as shown )

And If below the table , there are infinitely many **ants** are eating their food !

Then Find The **Maximum** velocity of Cube so that **No ant get Hurt** !

If Maximum Velocity can be expressed as :

\({ V }_{ o,max }\quad =\quad \sqrt { \cfrac { a(\sqrt { b } -c) }{ d } gL } \).

Then Find value of : " a + b + c + d " ? ?

**Details And Assumptions**

\(\bullet\) gcd(a,d) = 1 & gcd(a,c) = 1 & gcd (c,d)=1 & 'b' is square free integer.

\(\bullet\) Ant's are infinite in numbers and present at everywhere on the ground .

\(\bullet\) Assume If Cube Falls then ant's get Hurt .

Source : This is modified Form of an Similar Problem, which i got from my friend , we together make made this situation .