A bottle holder: A clever design of a bottle holder (a plank with a hole) is shown in the figure. Note that the holder is not fixed to the support; it stands freely, but only when the bottle is in. Assume that the mass of the bottle is 1 kg and that the center-of-mass of the bottle is at 3/5th of its length (h = 35 cm) from the neck support point. The bottle in its rest position is slightly tipped down (a = 15°). Assuming the mass of the stand to be negligible and l = 30 cm, find the angle 0 of the stand so that the bottle and the stand can be in equilibrium together as shown. 3h/5

A bottle holder: A clever design of a bottle holder (a plank with a hole) is shown in the figure. Note that the holder is not fixed to the support; it stands freely, but only when the bottle is in. Assume that the mass of the bottle is 1 kg and that the center-of-mass of the bottle is at 3/5th of its length (h = 35 cm) from the neck support point. The bottle in its rest position is slightly tipped down (a = 15°). Assuming the mass of the stand to be negligible and l = 30 cm, find the angle 0 of the stand so that the bottle and the stand can be in equilibrium together as shown. 3h/5