(a) $a_c = 40~m/s^2$ (b) $a_c = 80~m/s^2$
Work Step by Step
(a) $a_c = \omega^2~r$ If $r$ is doubled, then the centripetal acceleration is also doubled. The centripetal acceleration of the speck of dust that is twice as far away from the center is $40~m/s^2$. (b) $a_c = (2\omega)^2~r = 4\omega^2~r = 4\times(20~m/s^2)$ The centripetal acceleration would be $80~m/s^2$.