Question

in the below figure, where should the doorknob be located to make the door easier to open?

Explanation:

Torque ($\tau$) is given by $\tau = rF\sin\theta$, where $r$ is the distance from the axis of rotation, $F$ is the force, and $\theta$ is the angle between $r$ and $F$. To open the door easily, we want more torque. For a given force $F$ (and $\theta = 90^{\circ}$ for maximum $\sin\theta = 1$), increasing $r$ (distance from hinges) increases torque. So placing the doorknob far from the hinges (axis) gives more torque, making the door easier to open.

Answer:

The doorknob should be located as far as possible from the axis of rotation (the hinges), ideally at the opposite edge of the door from the hinges (e.g., the right - most edge of the door, horizontally speaking, regardless of vertical position in terms of the rotational principle, though in practice it's at a convenient height like shown but the key is maximum distance from the hinge axis).