Answer:
number of smaller disks in system B = 4
Step-by-step explanation:
Moment of Inertia of smaller disk is:
I_small = (1/2)MR²
Moment of inertia of larger disk is;
I_large = (1/2)M(2R)² = 2MR²
Now total moment of Inertia of system A will be 2 of the larger disk I_large
Thus, I_A = 2 x (2MR²) = 4MR²
While moment of inertia of system B will consist of 1 number of larger disk and n number of smaller disk.
Thus;
I_B = 2MR² + n((1/2)MR²)
Thus, I_B = MR²(2 + (n/2))
Since the two systems have equal moment of inertia, we will ewuate I_A to I_B. Thus,
I_A = I_B gives;
4MR² = MR²(2 + (n/2))
MR² will cancel out to give ;
4 = 2 + (n/2)
n/2 = 4 - 2
n/2 = 2
n = 4