Final answer:
The torque exerted by a force 20ˆj N applied at r=(4.0ˆi−2.0ˆj)m about the origin is calculated using the cross product of the position vector and the force vector, resulting in a torque of 80 Nm, which is not among the provided options.
Step-by-step explanation:
The question asks about the torque exerted by a force around a given point, which is a concept in physics related to the rotational effect of a force. To calculate the torque we use the cross product of the force vector and the position vector, represented as τ = r × F. In this case, the force is 20ˆj N and the position vector is r=(4.0ˆi−2.0ˆj)m. The torque about the origin can be calculated by taking the cross product of the position vector and the force vector:
τ = (4.0ˆi - 2.0ˆj) m × 20ˆj N = (4.0 × 20) k Nm - (-2.0 × 20) i Nm
The i component doesn't contribute to the torque about the z-axis, so we only consider the k component which gives us τ = 80 Nm in the k direction, meaning out of the page.
Therefore, the correct answer would be that the torque about the origin is not listed in the given options since 80 Nm is not an option provided in the question. The student is encouraged to review the options or the calculations again.