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If F be a force acting on a particle having the position vector r and $τ$ be the torque of this force about the origin, then

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$r \cdot τ \neq 0 and F \cdot τ \neq 0$

$r \times τ \neq 0 and F \times τ = 0$

$r \cdot τ = 0 and F \cdot τ = 0$

$r \times τ = 0 and F \times τ \neq 0$

answer is A.

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Detailed Solution

Torque, $τ = r \times F$ , i.e. $τ$ is perpendicular to both r and F.

$∴ r \cdot τ = 0 and F \cdot τ = 0$

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