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

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)