A wheel of radius $R$ and mass $M$ is placed at the bottom of a fixed step of height $R$ as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $\tau$ about an axis normal to the plane of the paper passing through the point $Q$. Which of the following options is/are correct?

Step 1: Define the torque about the corner $Q$.

The torque $\tau$ about the fixed corner $Q$ is the product of the force and its perpendicular distance $d$ from $Q$.

$$\tau = F \cdot d$$

Step 2: Analyze the tangential force at $P$.

The line of action of a tangential force at $P$ is at a constant distance of $2R$ from $Q$.

$$d = 2R$$ $$\tau = 2FR$$

Since the torque remains constant, Option 1 is incorrect.

Step 3: Analyze the normal force at $X$.

Any normal force on the wheel passes through its center, which is always at a distance $R$ from $Q$.

$$d = R$$ $$\tau = FR$$

Since the torque remains constant, Option 2 is correct.

Step 4: Analyze the normal force at $P$.

The line of action of a normal force at $P$ passes directly through the center and the corner $Q$.

$$d = 0$$ $$\tau = 0$$

Thus, Option 3 is correct.

Step 5: Analyze the tangential force at $S$.

The line of action of a tangential force at $S$ is at a distance $R$ from $Q$.

$$d = R$$ $$\tau = FR \neq 0$$

Since a sufficiently large force can make the wheel climb, Option 4 is incorrect.

Answer: Correct options are (2) and (3).