Asmall 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. the ball makes 2.0 revolutions every 1.0 s. what are the magnitude and direction of the acceleration of the ball?

Centripetal acceleration = (speed²) / (radius of the curve).

-- Radius of the circle in this question = 0.5 meter
-- Circumference = (diameter) x (π)  =  π meters

-- Speed of the ball on the circle = (2 circumferences / sec) = 2π m/s

Centripetal acceleration = (2π)² / 0.5  =  78.96 m/s²

                                                          (about 8.05 g)

The acceleration is directed toward the center of the circle.

To answer the questions that are asked, we don't need to know
the mass of the ball that's revolving.  We'd only need to know it
if we were asked to find the centripetal force ... the force on the
ball that keeps it on the circular path, i.e. the tension in the string.

Learned about life itself

Divide 108.2 x 10^6 into 1.5 x 10 and the result will be in au (astronomical units)