MCQ
A disc is rotating with angular velocity $\vec{\omega}$. A force $\vec{F}$ acts at a point whose position vector with respect to the axis of rotation is $\vec{r}$. The power associated with torque due to the force is given by ..........
  • $(\vec{r} \times \vec{F}) \cdot \vec{\omega}$
  • B
    $(\vec{r} \times \vec{F}) \times \vec{\omega}$
  • C
    $\vec{r} \times(\vec{F}, \vec{\omega})$
  • D
    $\vec{r} \cdot(\vec{F} \times \vec{\omega})$

Answer

Correct option: A.
$(\vec{r} \times \vec{F}) \cdot \vec{\omega}$
a
(a)

$\text { power } =\vec{F} \cdot \vec{v}$

$=\vec{F} \cdot(\vec{r} \times \vec{w})$

$=[\vec{F} \vec{r} \vec{w}]$
$=[\vec{r} \vec{F} \quad \vec{w}]$

$=\vec{r} \cdot(\vec{F} \times \vec{w})$

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