The correct question is:
A 130 g ball and a 230 g ball are connected by a 34-cm-long, massless, rigid rod. The balls rotate about their center of mass at 120 rpm .
What is the speed of the 130 g ball?
Answer:
Speed = 2.728 m/s
Explanation:
Center of mass is the point where weighted mass in a system of bodies is equal to zero. At this point, when force is applied it results in linear motion and not angular motion.
The distance from the objects to the center of mass is proportional to their weights (that is weighted relative position).
m1= 130g/1000= 0.13 kg
m2= 230g/1000= 0.23 kg
r= 34cm/100= 0.34 m
m1r1 = m2r2
r2= r-r1
Thus m1r1 = m2(r-r1)
130*r1 = 230*(0.34-r1)
130*r1= 78.2 - 230*r1
230r1+130r1 = 78.2
360r1= 78.2
r1= 78.2/360
Effective radius of 130g ball ( r1)= 0.217 m
Circumference= 2πr
= 2*3.14*0.217
= 1.364 m
RPM= 120rpm/60= 2 rotations per second(rps)
Thus speed of 130g ball= r1 * circular speed (rps)
= 1.364 * 2
Speed = 2.728 m/s
