A ball of mass ‘$m$’ is rotating in a circle of radius ‘$r$’ with speed $v$ inside a smooth cone as shown in figure.

Let $N$ be the normal reaction on the ball by the cone, then choose the correct option.

Vertical component of normal reaction balances the weight of the ball .

So N  cos $\theta$ = mg

Also acceleration of the ball is $\frac{v^2}{r} and it is horizontal .$Component of this acceleration along the curved surface of the cone = $\frac{v^2}{r} \cos \theta .$

Resultant force acting on the ball along the curved surface = mg sin $\theta .$

Therefore , m$\times \frac{v^2}{r}\cos \theta = mg \sin \theta \Rightarrow \frac{v^2}{r}\cos \theta = g \sin \theta$

Also net horizontal force acting on the ball = N sin $\theta$

So N $\sin \theta = \frac{m{v}^2}{r}$