Two identical dumbbells (having point masses at end) of length $\ell$ are connected by an axle situated at the midpoint of their lengths and are placed on a frictionless horizontal plane in vertical position. A small impulse is imparted to each body at the bottom in the opposite directions so that both dumbbells will rotate vertically and reach the horizontal position.

The velocity of the mass which is initially at the top, relative to the one on the plane on the same dumbbell at the moment when the dumbbells reach the horizontal position is $\sqrt{2\mathrm{g\ell }}$

The velocity of the mass which is initially at the top, relative to the one on the plane on the same dumbbell at the moment when the dumbbells reach the horizontal position is$\sqrt{\mathrm{g\ell }}$

Centre of mass of system initially at rest will not move horizontally

Now we assume that friction exists between the plane and the bodies of the dumbbells. The angle $\mathrm{\alpha }$ made by dumbbells relative to the horizontal when the system can start moving by itself is given by $\tan \mathrm{\alpha }=\mathrm{\mu }$. The coefficient of friction $\mathrm{\mu }$  is known.