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. The bottle in its rest position is slightly tipped up $(α = 15^{0})$ . Assume the mass of the holder to be negligible and $l = 24 c m$ , and the angle $θ = 53^{0}$ . Then the distance of COM of the bottle from the hole (x (in cm)) so that the bottle and the holder can stand together as shown is ______ (Take $\cos 15^{0} = 24 / 25$ ).

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answer is 15.

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Detailed Solution

Mg and N must be concurrent.
$N = M g$
Torque about hole $m g x \cos α = N l \cos θ$

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