NAEST 2020: Balance the hairband from different points on a

Question: The hairband can be balanced by supporting it at various points. For each such point, it stays in a particular orientation. Choose the correct option(s).

1. For different orientations of the hairband, it has different positions of the centre of mass.
2. The hairband cannot be supported at its centre of mass.
3. The vertical line through the point of support cuts the hairband at different points for its different orientations.
4. The vertical line through the point of support passes through a fixed point in space for any orientation of the hairband.

Solution: The centre of mass of the hairband is fixed. The centre of mass lies in an empty space somewhere close to the geometric centre of the hairband. Hence, options (A) and (B) are wrong.

Option (C) is correct as the vertical line through the point of support cuts the hairband at different points for its different orientations.

The vertical line through the point of support always passes through the centre of mass of the hairband. The centre of mass remains fixed relative to the hairband. But the centre of mass move in space as the performer translates the hairband. Thus, option (D) is not correct.

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