The ratio of their moments of inertia about the axes passing through their centers and perpendicular to their planes, will be 2:1 (Option B).
How to calculate the ratio of their moments?
The moment of inertia I of a body rotating about an axis is given by the formula;
I = ¹/₂mr²
where;
- m is the mass
- r is the radius
For a circular disc with mass m and radius R, the moment of inertia I₁ about an axis passing through its center and perpendicular to its plane is;
I₁ = ¹/₂mR²
For a circular ring with mass m and radius R, the moment of inertia I₂ about an axis passing through its center and perpendicular to its plane is;
I₂ = mR²
The ratio of moment of inertia of ring to moment of inertia of disc is;
= I₂ / I₁
= (mR²) / (¹/₂mR²)
= (1) / (1/2)
= 2/1
= 2 : 1