Which of the following are correct expression | vedclass

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(C) The torque $\vec{	au}$ is defined as the rate of change of angular momentum: $\vec{	au} = \frac{d\vec{L}}{dt}$.Since $\vec{L} = \vec{r} 	imes \

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$B, C, D$ and $E$ Only

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(C) The torque $\vec{	au}$ is defined as the rate of change of angular momentum: $\vec{	au} = \frac{d\vec{L}}{dt}$.Since $\vec{L} = \vec{r} 	imes \vec{p}$,expression $B$ is correct: $\vec{	au} = \frac{d}{dt}(\vec{r} 	imes \vec{p})$.Using the product rule: $\frac{d}{dt}(\vec{r} 	imes \vec{p}) = (\frac{d\vec{r}}{dt} 	imes \vec{p}) + (\vec{r} 	imes \frac{d\vec{p}}{dt})$.Since $\frac{d\vec{r}}{dt} = \vec{v}$ and $\vec{p} = m\vec{v}$,the term $(\vec{v} 	imes m\vec{v}) = 0$. Thus,$\vec{	au} = \vec{r} 	imes \frac{d\vec{p}}{dt}$,so expression $C$ is correct.Since $\frac{d\vec{p}}{dt} = \vec{F}$,expression $E$ is correct: $\vec{	au} = \vec{r} 	imes \vec{F}$.For a rigid body rotating about a fixed axis,$\vec{	au} = I\vec{\alpha}$,so expression $D$ is correct.Expression $A$ is incorrect as $\vec{	au} = \frac{d\vec{L}}{dt}$,not $\vec{r} 	imes \vec{L}$.Therefore,$B, C, D,$ and $E$ are correct.

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