Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

Question

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be (A) 5I (B) 3I (C) 6I (D) 4I

Tardigrade Admin · Accepted Answer

Moment of inertia of uniform circular disc about diameter

= I

According to theorem of perpendicular axes.
Moment of inertia of disc about axis

= 2 I = \frac{1}{2} m r^{2}

Applying theorem of parallel axes
Moment of inertia of disc about the given axis

= 2 I + m r^{2} = 2 I + 4 I = 6 I

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Q. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

5I

3I

6I

4I

Moment of inertia of uniform circular disc about diameter =I According to theorem of perpendicular axes. Moment of inertia of disc about axis =2I=21​mr2 Applying theorem of parallel axes Moment of inertia of disc about the given axis =2I+mr2=2I+4I=6I.

Q. Moment of inertia of a uniform circular disc about a diameter is $I$ . Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

Moment of inertia of uniform circular disc about diameter $= I$
According to theorem of perpendicular axes.
Moment of inertia of disc about axis $= 2 I = \frac{1}{2} m r^{2}$
Applying theorem of parallel axes
Moment of inertia of disc about the given axis
$= 2 I + m r^{2} = 2 I + 4 I = 6 I$ .