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In the expression →r×→F can |→r| ever be less than the lever arm? Can it be equal to the lever arm?

a) Yes, No.
b) No, Yes.
c) Yes, Yes.
d) No, No.

1 Answer

2 votes

Final answer:

In the context of torque, |→r| can be less than the lever arm if the force is not acting perpendicularly and it can be equal to the lever arm when the force acts perpendicular to →r. Therefore, the answer is Yes, Yes.

Step-by-step explanation:

The question focuses on torque, the cross product of the position vector (→r) and the force vector (→F), and the relationship between the magnitudes of →r and the lever arm. The lever arm is defined as the perpendicular distance from the pivot point to the line of action of the force. The magnitude of →r (|→r|) can be equal to the lever arm when the force acts perpendicularly to →r. If the force does not act perpendicularly, the lever arm will be less than the magnitude of →r, as it is the shortest distance to the line of action of the force.

Thus, the correct answer to whether the magnitude of →r can ever be less than the lever arm is Yes, because it depends on the angle at which the force is applied. It can also be equal to the lever arm when the force is applied perpendicularly. Hence, the correct answer is c) Yes, Yes.

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