$Hint:$ Use the Newton's second law to balances the forces in $x$ and $y$ directions.

$Step\,1:$ Draw the free body diagram of the system.

Step 2:Balance the forces in horizontal and vertical direction. Balancing forces along vertical direction.

$N \cos \theta=m g$

Balancing forces along horizontal direction.

$\Sigma F _{ nes }=m\left( a _2\right)$

$N \sin \theta=m\left(\omega^2 r\right)$

Here, $r=r \sin \theta$.

$N$ is the normal reaction, $m$ is the mass of the block and $g$ is the acceleration due to gravity.

Step $3$: Solve the equations.

Dividing equation $1$ and $2$ and using equation $3$ , we get:

$\omega=\sqrt{\frac{g}{r \cos \theta}}$