Engineering
Physics
Center of Mass
Question

A stick is thrown in the air and lands on the ground at some distance from the thrower. The centre of mass of the stick will move along a parabolic path

in all cases

only if the stick has a shape such that its centre of mass is located at some point on it and not outside it.

only if the stick has linear motion but no rotational motion

only if the stick is uniform

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Solution

The center of mass of any object, regardless of its shape, mass distribution, or rotation, follows a parabolic trajectory under constant gravity when air resistance is negligible. This is because the net external force (gravity) acts at the center of mass, causing it to accelerate downward at g. The motion can be separated into independent horizontal (constant velocity) and vertical (constant acceleration) components, which combine to form a parabola. The stick's rotation or non-uniformity does not affect this path.

Final answer: in all cases