Understand the setup

A block moves in a horizontal circular groove and touches the vertical wall of the groove.

• The wall exerts a normal reaction $N$ horizontally toward the center of the circular path.
• Since the groove is smooth, there is no friction.
• Vertically, the weight $mg$ is balanced by the normal reaction from the bottom surface, so vertical motion is irrelevant here.

Identify the force providing centripetal acceleration

For circular motion of radius $r$, the required centripetal force is $F_c = \frac{mv^2}{r}.$

The only horizontal radial force is the normal reaction by the vertical wall. Hence, $N = \frac{mv^2}{r}.$

Relation between $N$ and $v$

Therefore, $N \propto v^2.$

So the graph of $N$ versus $v$ is:

• passing through the origin,
• increasing with $v$,
• a parabola opening upward.

Choose the correct option

The correct curve is the one representing $N = \frac{m}{r}v^2.$

That corresponds to Option A.

Comparison with stored answer

Stored correct answer: A

Derived answer: A

Hence, they agree.