The radius of the path of an object in uniform circular motion is halved. The centripetal acceleration needed, given that
its speed remains the same, is
half as great
the same as before
twice as great as before
four times as great as before

twice as great as before

Explanation:

recall that centripetal acceleration is given by

let the original radius of the circular motion = r₁ and the reduced radius be =r₂

acceleration for original radius, a₁ = v² / r₁   ==> v²=a₁ r₁

acceleration for reduced radius, a₂ = v² / r₂   ==> v²=a₂ r₂

given that the speed remains the same, we can equate the two expressions above

a₁ r₁ = a₂ r₂  (rearranging)

a₂ = (r₁ / r₂) a₁

we are given that r₂ = 1/2 r₁  (substitute this into equation)

a₂ = (r₁ / r₂) a₁

a₂ = [r₁ / (1/2)r₁ ] a₁

a₂ = [r₁ / (1/2)r₁ ] a₁

a₂ = 2a₁

hence we can see that the acceleration of the path with the smaller raidus has an acceleration that is twice the original

moving ball hits still ball. mover stops, hit ball moves. momentum transfer.

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.