Question

part c
how does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point?

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the torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side and opposite in direction.
the torque due to the weight of the shorter side (the bristles of the broom) is larger in magnitude than the torque due to the weight of the longer side (the handle), and opposite in direction.
the torque due to the weight of the shorter side (the bristles of the broom) is smaller in magnitude than the torque due to the weight of the longer side, and opposite in direction.
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Explanation:

When an object is in rotational equilibrium (such as a broom balanced at a point), the sum of the torques about the balance - point is zero. Torque is calculated as $\tau = rF\sin\theta$. For the broom, the weight of each side acts at its center - of - mass. Since the broom is balanced, the torques exerted by the weights of the two sides about the balance point must be equal in magnitude and opposite in direction to satisfy the condition of rotational equilibrium ($\sum\tau=0$).

Answer:

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side and opposite in direction.