Answer:
I will say the first one
Step-by-step explanation:
From the figure, we can see that the assembly consists of two circular discs of different masses and radii, which are rigidly fixed to a massless, rigid rod of length √24 a through their centers. The assembly is set rolling without slipping on a flat surface, and the angular speed about the axis of the rod is co. The angular momentum of the entire assembly about the point 'O' is L.
We can use the conservation of angular momentum to answer the question. Since there is no external torque acting on the system, the angular momentum of the system about point 'O' is conserved. Therefore, the initial angular momentum of the system must be equal to the final angular momentum of the system.
The initial angular momentum of the system can be calculated as follows:
Li = I1 * w1 + I2 * w2
Where:
I1 = moment of inertia of the smaller disc about its center = (1/2) * m * a^2
w1 = angular speed of the smaller disc about its center = co
I2 = moment of inertia of the larger disc about its center = (1/2) * 4m * (2a)^2 = 8ma^2
w2 = angular speed of the larger disc about its center = 0 (since the larger disc is not rotating about its center)
Therefore, the initial angular momentum of the system is:
Li = (1/2) * m * a^2 * co + 8ma^2 * 0
Li = (1/2) * m * a^2 * co
The final angular momentum of the system can be calculated as follows:
Lf = I * wf
Where:
I = moment of inertia of the entire assembly about point 'O' = (1/2) * m * a^2 + (4/3) * m * (2a)^2 = (22/3) * ma^2
wf = final angular speed of the entire assembly about point 'O'
Therefore, the final angular momentum of the system is:
Lf = (22/3) * ma^2 * wf
Since the initial angular momentum must be equal to the final angular momentum, we can equate Li and Lf and solve for wf:
(1/2) * m * a^2 * co = (22/3) * ma^2 * wf
wf = (3/44) * co
Therefore, the final angular speed of the entire assembly about point 'O' is (3/44) times the initial angular speed about the axis of the rod.
From the given options, we can see that statement (i) is true, which states that the final angular speed of the entire assembly is less than the initial angular speed about the axis of the rod. Statement (ii) is false, since the final kinetic energy of the entire assembly is less than the initial kinetic energy about the axis of the rod, due to the work done against friction. Therefore, the correct answer is (i) only.