A force F ⃗ \vec{F} F =(2î+3ĵ) N is applied at position r ⃗ \vec{r} r =(4î+5ĵ) m to an object pivoted about the z-axis. Which option correctly gives both the magnitude and direction of the torque about the z-axis?
Physics · Rotational Motion · torque and rotational equilibrium
JEE Advanced

Question

A force F ⃗ \vec{F} F =(2î+3ĵ) N is applied at position r ⃗ \vec{r} r =(4î+5ĵ) m to an object pivoted about the z-axis. Which option correctly gives both the magnitude and direction of the torque about the z-axis?

Physics · Rotational Motion · torque and rotational equilibrium

G1 Physics · Accepted Answer

Torque is τ⃗=r⃗×F⃗. With r⃗=(4î+5ĵ) m and F⃗=(2î+3ĵ) N, the component along z is 4×3-5×2=2 N·m. Positive sign means +k̂ direction. Thus the result is 2.00 N·m, +k̂, option C.