Import Question JSON

$\text{Hint: } \tau = \vec{r} \times \vec{F}$ $\text{Step 1: Find the direction of the torque about the two axes.}$ $\text{Consider the adjacent diagram, where } r > r'$ $\text{Torque } \vec{\tau} \text{ about z-axis } = \vec{r} \times \vec{F} \text{ which is along } \hat{k}$ $\text{Torque } \vec{\tau}' \text{ about z'-axis } = \vec{r}' \times \vec{F} \text{ which is along } -\hat{k}$ $\text{Step 2: Find the magnitude of the torque about the two axes.}$ $|\vec{\tau}|_z = Fr_\perp = \text{the magnitude of the torque about the z-axis}$ $\text{where } r_\perp \text{ is the perpendicular distance between F and z-axis.}$ $\text{Similarly, } |\vec{\tau}'|_{z'} = Fr'_\perp$ $\text{Clearly, } r_\perp > r'_\perp \Rightarrow |\vec{\tau}|_z > |\vec{\tau}'|_{z'}$ $\text{We are always calculating resultant torque about a common axis.}$ $\text{Hence, total torque } \vec{\tau}'_{net} \neq \vec{\tau} + \vec{\tau}' \text{, because } \vec{\tau} \text{ and } \vec{\tau}' \text{ are not about a common axis.}$ $\text{Therefore, statements (b) and (c) are correct.}$