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, bur 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 `(alpha 15^@)`. Assuming the mass of the holder to be negligible and `l = 24 cm`, and the angle `theta = 53^@`. Find the distance of `COM` of the bottle from the hole `(x)` so that the bottle and the holder can stand together as shown. (Take `cos 15^@ = 24//25`). Express your answer on `cm`.
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Answer

`0015`

Explanation

Torque about point of contact should be zero. Torque may be only of weight of bottle. For torque of `m` to be zero line of action of `mg` should pass through point of contact.

`x cos 15^@ = l cos 53^@`
`x xx (24)/(25) = 24 xx (3)/(5)`
`x = 15 cm`.