Question

the circles radius in case b is twice that of case a. the speed is the same in each case. how does the acceleration in case a compare to the acceleration in case b? case a case b the acceleration in case a is... tap to select answer.... the acceleration of case b.

Explanation:

Step1: Write the formula for centripetal acceleration

The formula for centripetal acceleration \(a = \frac{v^{2}}{r}\).

Step2: Calculate acceleration for Case A

For Case A, \(a_{A}=\frac{v^{2}}{R}\).

Step3: Calculate acceleration for Case B

For Case B, \(r = 2R\), so \(a_{B}=\frac{v^{2}}{2R}\).

Step4: Compare \(a_{A}\) and \(a_{B}\)

We find \(\frac{a_{A}}{a_{B}}=\frac{\frac{v^{2}}{R}}{\frac{v^{2}}{2R}} = 2\), so \(a_{A}=2a_{B}\).

Answer:

The acceleration in Case A is twice the acceleration of Case B.