Final answer:
The angular velocity of the system can be found using the conservation of angular momentum and the moments of inertia of the balls. The angular velocity is approximately 1.55 rad/s. Hence, the correct answer is option (a).
Step-by-step explanation:
The angular velocity of a system is the rate at which the system rotates. To find the angular velocity of the system, we need to consider the conservation of angular momentum. Angular momentum is conserved when no external torques are acting on the system.
In this case, the balls are connected by a massless, rigid rod, so we can assume no external torques. Therefore, the initial angular momentum of the system is equal to the final angular momentum:
Angular momentum before = Angular momentum after
Angular momentum = inertia * angular velocity
The inertia of the system can be calculated by summing the moments of inertia of the two balls about the center of mass of the system:
Inertia = inertia of ball 1 + inertia of ball 2 = m1 * r1^2 + m2 * r2^2
Where m1 and m2 are the masses of the balls and r1 and r2 are their distances from the center of mass. The angular velocity of the system can then be calculated by rearranging the equation:
Angular velocity = angular momentum / inertia
Plugging in the given values (m1 = 110 g, m2 = 220 g, r1 = r2 = 31 cm), we get:
Angular velocity = angular momentum / (110 g * (31 cm)^2 + 220 g * (31 cm)^2)
Converting grams to kilograms and centimeters to meters, and calculating the angular velocity, we find that the angular velocity of the system is approximately 1.55 rad/s.