6.System of Particles and Rotational Motion
medium

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 ..........

A

$(\vec{r} \times \vec{F}) \cdot \vec{\omega}$

B

$(\vec{r} \times \vec{F}) \times \vec{\omega}$

C

$\vec{r} \times(\vec{F}, \vec{\omega})$

D

$\vec{r} \cdot(\vec{F} \times \vec{\omega})$

Solution

(a)

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

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

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

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

Standard 11
Physics

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