# Aditya's challenges in Mechanics 6

In the figure above,there is dumb-bell of mass $$m=2.5 \text{ kg}$$ which is rolling without slipping on a rough horizontal surface with a velocity $$v$$. The horizontal merges into an incline which subtends an angle $$A$$ with the horizontal in clock-wise direction. Find the minimum value of $$A$$ for which the dumb-bell gets separated from the horizontal surface for any velocity $$v$$.

If $$A$$ can be expressed as $$A=\arcsin { \left( \dfrac { \sqrt { P } }{ Q } \right) }$$, where $$P$$ is not a perfect square integer, find $$P+Q$$.

Consider the dumb-bell as 2 light spheres connected to a heavy axle.

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