Question

As shown in the figure, two thin coplanar circular discs A and B each of mass 'M' and radius 'r' are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc B and passing through its centre is

• A. $2Mr^2$
• B. $3Mr^2$
• C. $4Mr^2$
• D. $5Mr^2$

Hint:

Parallel axis theorem: $I = I_{cm} + Md^2$.

Answer 1

The Correct Option is D

The moment of inertia of disc B about an axis perpendicular to its plane and passing through its center is $I_B = \frac{1}{2}Mr^2$. For disc A, we use the parallel axis theorem. The moment of inertia of disc A about its own center is $\frac{1}{2}Mr^2$. The distance between the axis of rotation (center of B) and the center of A is $2r$. So, $I_A = \frac{1}{2}Mr^2 + M(2r)^2 = \frac{1}{2}Mr^2 + 4Mr^2 = \frac{9}{2}Mr^2$. The moment of inertia of the system is $I = I_A + I_B = \frac{9}{2}Mr^2 + \frac{1}{2}Mr^2 = 5Mr^2$.