Acceleration vector making an angle of 30degree with velocity vector means tangential acceleration is in the direction of rotation of disc and centripetal towards the centre.
so centripetal acceleration (Ac)/ tangential acceleration (At) = Asin30degree/Acos30degree=1/√3.

Introduction:
In this problem, we have a rotating disc and we are given that a point on the periphery of the disc has an acceleration vector making an angle of 30 degrees with the velocity vector. We need to find the ratio of the centripetal acceleration to the tangential acceleration.

Understanding the problem:
To solve this problem, we need to understand the concepts of centripetal acceleration and tangential acceleration. Centripetal acceleration is the acceleration experienced by an object moving in a circular path towards the center of the circle. Tangential acceleration, on the other hand, is the component of acceleration tangent to the circular path.

Approach:
To find the ratio of centripetal acceleration to tangential acceleration, we need to determine the magnitudes of both accelerations and then calculate their ratio.

Solution:
Let's assume that the magnitude of the velocity vector is v.

Step 1: Finding the magnitude of the centripetal acceleration:
The centripetal acceleration is given by the formula:

ac = v^2 / r

where ac is the centripetal acceleration and r is the radius of the circular path.

Step 2: Finding the magnitude of the tangential acceleration:
The tangential acceleration can be calculated using the formula:

at = a * sinθ

where at is the tangential acceleration, a is the magnitude of the acceleration vector, and θ is the angle between the acceleration vector and the velocity vector.

In this case, θ = 30 degrees. Therefore, the tangential acceleration becomes:

at = a * sin30 = (a * √3) / 2

Step 3: Calculating the ratio:
The ratio of the centripetal acceleration to the tangential acceleration can be found by dividing the magnitude of the centripetal acceleration by the magnitude of the tangential acceleration:

Ratio = ac / at = (v^2 / r) / ((a * √3) / 2)

Simplifying the expression, we get:

Ratio = (2v^2) / (a * √3 * r)

Conclusion:
The ratio of the centripetal acceleration to the tangential acceleration is given by (2v^2) / (a * √3 * r), where v is the magnitude of the velocity vector, a is the magnitude of the acceleration vector, and r is the radius of the circular path.