You observe two galaxy clusters, cluster A and cluster B.Both have the same radius, but cluster B's outer galaxies are orbiting the cluster with circular velocities that are twice that of cluster A's circular velocities.The mass of cluster B is
A) 2 times cluster A's mass
B) 4 times cluster A's mass.
C) half of cluster A's mass.
D) one-quarter of cluster A's mass.
E) equal to cluster A's mass.

Question

Quizplus · Accepted Answer

The mass of a galaxy cluster can be determined using the formula for circular velocity: $v^2 = \frac{GM}{r}$. Since the velocities are squared, if cluster B's velocities are twice that of cluster A, then the mass of cluster B must be four times that of cluster A to maintain the same radius.

You Observe Two Galaxy Clusters, Cluster a and Cluster B