Suppose Earth had no atmosphere and a ball were fired from the surface in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around the earth, the ball’s acceleration would be ?

Can you please describe the ans... I would be glad to know about it .

To answer this, I would need to know the terms you were taught in physics.

The simplest terms I know:
Acceleration - A change in direction and/or speed of an object.
Centripedal Acceleration - The rate of change in the velocity of an object on a tangent path.
LINK
You can use the equations on that page to calculate your Centripedal Acceleration.

If you were taught in different terms, or do not understand what is on that page, I'll be glad to help more, just post back.

a=F/m ( use F=ma in the direction to center of earth)
=(mg)/m
=g( gravitational acceleration at that place)

All the acceleration would be centripetal acceleration (acceleration toward the center of the earth).

That would be acceleration due to gravity, yes?