Which of the following are correct expressions for torque acting on a body?
A. $\vec{\tau }=\vec{\mathrm{r}}\times \vec{\mathrm{L}}$
B. $\vec{\tau }=\frac{\mathrm{d}}{\mathrm{dt}}(\vec{\mathrm{r}}\times \vec{\mathrm{p}})$
C. $\vec{\tau }=\vec{\mathrm{r}}\times \frac{\mathrm{d}\vec{\mathrm{p}}}{\mathrm{dt}}$
D. $\vec{\tau }=\mathrm{I}\vec{\alpha }$
E. $\vec{\tau }=\vec{\mathrm{r}}\times \vec{\mathrm{F}}$
( $\vec{\mathrm{r}}=$ position vector; $\vec{\mathrm{p}}=$ linear momentum; $\vec{\mathrm{L}}=$angular momentum; $\vec{\alpha }=$angular acceleration; $\mathrm{I}=$moment of inertia; $\vec{\mathrm{F}}=$ force; $\mathrm{t}=$ time)
Choose the correct answer from the options given below :

Question

YESPYQ · Accepted Answer

Correct answer: c) B, C, D and E Only. $\vec{\tau }=\vec{r}\times \vec{L}$ This relation is incorrect in general because torque is not the cross product of position vector and angular momentum. $\vec{\tau }=\frac{d}{dt}\left(\vec{r}\times \vec{p}\right)$ This is correct and represents the fundamental definition of torque. Using Newton’s second law, the time derivative of momentum equals force. $\vec{\tau }=\vec{r}\times \frac{d\vec{p}}{dt}=\vec{r}\times \vec{F}$ This form is correct and commonly used in mechanics. $\vec{\tau }=I\vec{\alpha }$ This relation is correct for rigid bodies rotating about a fixed axis.

Which of the following are correct expressions for torque acting on a body? A. \(\vec{\tau }=\vec{\mathrm{r}}\times \vec…

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