Question

# If →F is a force acting on a particle having the position vector →r and →τ is the torque due to this force about the origin, then-

A
rτ=0
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B
rτ0
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C
Fτ=0
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D
Fτ0
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Solution

## The correct option is C →F⋅→τ=0As we know that cross product of the two vectors is always perpendicular to both individual vectors. Torque on the particle about origin is, →τ=→r×→F So, →τ⊥(→r and →F) →r⊥(→r×→F); →F⊥(→r×→F) ∴→r⋅→τ=→r⋅(→r×→F)=0 →F⋅→τ=→F⋅(→r×→F)=0 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, options (A) and (C) are the correct answer. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Why this question ? This question involves the idea of torque on a particle. Torque is always perpendicular to the plane formed by force vector and position vector.

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