Question

The torque of the force about O is defined as tau=r×F, then
A.) R. F must be zero
B.) Tau. F must be non zero
C.) Tau. (r-F) must be zero
D.) Tau. R must be non zero

Answer 1

torque is cross product of radius vector and force vector. it means, torque is perpendicular upon plane of radius vector as well as force vector.

so, $\vec{\tau}.\vec{r}=0$

and $\vec{\tau}.\vec{F}=0$

and also $\vec{\tau}.\vec{r}-\vec{\tau}.\vec{F}=0$

or, $\vec{\tau}.(\vec{r}-\vec{F})=0$

hence, $\vec{\tau}.(\vec{r}-\vec{F})=0$ must be zero.

therefore, option (D) is correct.