You balance a broom horizontally on your finger in such a way that your finger was exactly on the broom's center of gravity.

Now, if you marked that spot and cut the broom in two, then you would have a long and a short piece.

The long piece constitutes most of the handle and the short piece being bristle and a small part of the handle.

Which will now weigh more: the short piece or the long piece or, will they weigh the same? Give reasons for your answer.

The bristle piece will weigh more. The handle piece requires less mass to balance the torque of the bristle piece because much of its mass is at a larger radial distance from the fulcrum. The total torque on each side is the integral of r dm g, where r is the radius, dm is the incremental unit of mass with radius, and g is the acceleration of gravity. (dm g) provides the downward force for each component of torque, r F.

Posted by Steven Lord on 2022-03-19 08:42:50