Answer:
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
[tex]a = \dfrac{v^2}{r}[/tex]
v represents the linear velocity and r the radius of motion.
For object A, let its radial acceleration be [tex]a_A[/tex], its linear velocity be v and its radius of motion be r. Then
[tex]a_A = \dfrac{v^2}{r}[/tex]
For object B, let its radial acceleration be [tex]a_B[/tex]. It has the same linear velocity, v, as object A and its radius of motion is 4 times that of object A, 4r. Then
[tex]a_B = \dfrac{v^2}{4r} = \frac{1}{4}\left(\dfrac{v^2}{r}\right)[/tex]
But the expression in parentheses is [tex]a_A[/tex].
[tex]\therefore a_b = \dfrac{a_A}{4}[/tex]
[tex]a_A = 4a_B[/tex]
Hence, the radial acceleration of object A is 4 times that of object B.
