Two material points move along a circle with radii R1 = R and R2 = 2R with the same periods

Two material points move along a circle with radii R1 = R and R2 = 2R with the same periods. Compare their centripetal accelerations.

Given:

T1 = T2 = T – the periods of rotation of material points are the same;

R1 = R;

R2 = 2 * R;

pi is a geometric constant.

It is required to compare the centripetal accelerations of material points a1 / a2.

The centripetal acceleration of the first point is:

a1 = 4 * pi ^ 2 * R1 / T1 = 4 * pi ^ 2 * R / T.

The centripetal acceleration of the second point is:

a1 = 4 * pi ^ 2 * R2 / T2 = 4 * pi ^ 2 * 2 * R / T.

Then:

a1 / a2 = (4 * pi ^ 2 * R / T) / (4 * pi ^ 2 * 2 * R / T) =

= 4 * pi ^ 2 * R * T / (8 * pi ^ 2 * R * T) = 4/8 = 0.5.

Answer: a1 / a2 = 0.5 (correct answer: B) a1 = a2 / 2).