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If F⃗ is the force acting on a particle having position vector r⃗ and ? ⃗ be the torque

If F⃗ is the force acting on a particle having position vector r⃗ and ? ⃗ be the torque of this force about the origin, then:

Options

(a) r⃗ . ? ⃗ > 0 and F⃗ . ? ⃗ (b) r⃗ . ? ⃗ = 0 and F⃗ . ? ⃗ = 0
(c) r⃗ . ? ⃗ = 0 and F⃗ . ? ⃗ ≠ 0
(d) r⃗ . ? ⃗ ≠ 0 and F⃗ . ? ⃗ = 0

Correct Answer:

r⃗ . ? ⃗ = 0 and F⃗ . ? ⃗ = 0

Explanation:

? ⃗ = r⃗ x F⃗ ⇒ r⃗ . ? ⃗ = 0 and F⃗ . ? ⃗ = 0
Since, ? ⃗ is perpendicular to the plane of r⃗ and F⃗ , hence the dot product of ? ⃗ with r⃗ and F⃗ is zero.

AIPMT2009
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