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If F̅ is the force acting on a particle having position vector r̅ and τ̅ be the torque of this force about the origin, then:
- r̅ ⋅ τ̅ > 0 and F̅ ⋅ τ̅ < 0
- r̅ ⋅ τ̅ = 0 and F̅ ⋅ τ̅ = 0
- r̅ ⋅ τ̅ = 0 and F̅ ⋅ τ̅ ≠ 0
- r̅ ⋅ τ̅ ≠ 0 and F̅ ⋅ τ̅ = 0
Correct answer: r̅ ⋅ τ̅ = 0 and F̅ ⋅ τ̅ = 0
Solution
The torque τ̅ is defined as r̅ × F̅, which is a vector perpendicular to both r̅ and F̅. Therefore, the dot product r̅ ⋅ τ̅ and F̅ ⋅ τ̅ are both zero because the vectors involved are mutually perpendicular.
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