Moment of Inertia of a Disc about a Diameter
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The moment of inertia of a uniform circular disc about a diameter can be calculated using the formula:

I = (1/4) * m * r^2

where I is the moment of inertia, m is the mass of the disc, and r is the radius of the disc.

Moment of Inertia of a Disc about an Axis Perpendicular to its Plane
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When calculating the moment of inertia of a disc about an axis perpendicular to its plane and passing through a point on its rim, we can use the perpendicular axis theorem. According to this theorem, the moment of inertia about such an axis is equal to the sum of the moments of inertia of two perpendicular axes lying in the plane of the disc.

In this case, we can consider the moment of inertia about the diameter (which is perpendicular to the axis passing through the rim) and the moment of inertia about an axis passing through the center of the disc and perpendicular to its plane.

Using the formula for the moment of inertia of a disc about a diameter, we can say that the moment of inertia about the diameter is equal to I.

Moment of Inertia about an Axis Passing through the Center
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The moment of inertia of a disc about an axis passing through its center and perpendicular to its plane can be calculated using the formula:

I_center = (1/2) * m * r^2

where I_center is the moment of inertia about the center axis, m is the mass of the disc, and r is the radius of the disc.

Using the perpendicular axis theorem, we can sum the moments of inertia about the diameter and the center axis to find the total moment of inertia about the axis passing through the rim:

I_total = I + I_center

Substituting the expressions for I and I_center, we get:

I_total = (1/4) * m * r^2 + (1/2) * m * r^2
= (1/4 + 1/2) * m * r^2
= (3/4) * m * r^2

Comparing this with the original moment of inertia about the diameter (I), we can see that:

I_total = (3/4) * I

Therefore, the moment of inertia about an axis perpendicular to the disc's plane and passing through a point on its rim is 3/4 times the moment of inertia about the diameter.

In this question, it is given that the moment of inertia about the diameter is I. Therefore, the moment of inertia about an axis perpendicular to the disc's plane and passing through a point on its rim will be:

I_total = (3/4) * I

As the correct answer is option 'B', which corresponds to 6I, we can conclude that the moment of inertia about the perpendicular axis is indeed 6 times the moment of inertia about the diameter.