Object A and Object B are in uniform circular motion. If the linear velocities of both objects are equal, and the radius of the motion of Object. is 4 times the radius of the motion of Object A, the radial acceleration of Object A is how many times the radial acceleration of Object B?

The radial acceleration of object A is 4 times that of object B.

Explanation:

The radial acceleration, also known as centripetal acceleration, is given by

v represents the linear velocity and r the radius of motion.

For object A, let its radial acceleration be , its linear velocity be v and its radius of motion be r. Then

For object B, let its radial acceleration be . It has the same linear velocity, v, as object A and its radius of motion is 4 times that of object A, 4r. Then

But the expression in parentheses is .

Hence, the radial acceleration of object A is 4 times that of object B.