Which of the following are correct expression for torque acting on a body? A. $\vec{\tau}=\vec{r}\times\vec{L}$ B. $\vec{\tau}=\dfrac{d}{dt}(\vec{r}\times\vec{p})$ C. $\vec{\tau}=\vec{r}\times\dfrac{d\vec{p}}{dt}$ D. $\vec{\tau}=I\vec{\alpha}$ E. $\vec{\tau}=\vec{r}\times\vec{F}$

Question

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

Accepted Answer

(3) B, C, D and E Only. Options B, C, D, and E correctly express torque in different contexts: B relates torque to the rate of change of angular momentum, C connects torque to the change in linear momentum, D defines torque in terms of moment of inertia and angular acceleration, and E describes torque as the cross product of the position vector and force.

Solution

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