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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