Final answer:
The moment of inertia of a uniform circular disc about an axis perpendicular to its plane and passing through a point on its rim is 3I, using the parallel axis theorem. Therefore, the correct answer is d) 3I.
Step-by-step explanation:
The question asked is related to the concept of the moment of inertia in Physics, specifically for a uniform circular disc. The moment of inertia of a uniform circular disc about a diameter is given as I, and we are asked to find its moment of inertia about an axis perpendicular to its plane and through a point on its rim.
To find this, we use the parallel axis theorem, which states that the moment of inertia about any axis parallel to and a distance d away from an axis through the center of mass is Icenter + md².
The moment of inertia about the diameter (axis through the center) for a disc is MR²/4. The distance from the center to the rim is the radius R, so we apply the theorem as I = (MR²/4) + mR² = (MR²/4) + 4(MR²/4) = 5MR²/4 which is 1.25 times the moment of inertia about the central axis.
However, since we were given that the moment of inertia about the diameter is I, and not explicitly MR²/4, we can still use the parallel axis theorem in terms of I.
The parallel axis theorem would yield I + mR² (since the distance d equals the radius R). Since the moment of inertia of the disc about its center is half of that about the diameter, mR² equals 2I. Adding I (inertia about the diameter) to 2I (inertia of the parallel axis through the rim), we get 3I. Hence, the correct answer is d) 3I.