Two spheres each of mass M and radius R / 2 are connected...

Two spheres each of mass $M$ and radius $R / 2$ are connected with a massless rod of length $2 R$ as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod? (a) $\frac{21}{5} M R^{2}$ 5 (b) $\frac{2}{=} M R^{2}$ (c) $\frac{5}{2} M R^{2}$ (d) $\frac{5}{21} M R^{2}$

Two spheres each of mass $M$ and radius $R / 2$ are connected with a massless rod of length $2 R$ as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod?
(a) $\frac{21}{5} M R^{2}$
5
(b) $\frac{2}{=} M R^{2}$
(c) $\frac{5}{2} M R^{2}$
(d) $\frac{5}{21} M R^{2}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Composite Body Analysis

When dealing with systems made up of several individual bodies, the overall moment of inertia is found by summing the moments of inertia of the individual parts about the same axis. This additive property allows for the treatment of each component separately, adjusting for their positions relative to the axis (often using the parallel axis theorem), and then combining the results to obtain the total moment of inertia for the system.

Moment of Inertia

Moment of inertia is a measure of an object's resistance to angular acceleration, analogous to mass in linear motion. It depends on the distribution of the object's mass relative to the axis of rotation. This concept is central to analyzing rotational dynamics and calculating how different parts of a composite system contribute to the overall inertia about a given axis.

Parallel Axis Theorem

The parallel axis theorem is a critical tool used to determine the moment of inertia of an object about any axis parallel to an axis through its center of mass. It states that the moment of inertia about the new axis is equal to the moment of inertia about the center of mass plus the product of the mass and the square of the distance between the two axes. This theorem is essential for shifting reference axes in complex problems involving composite bodies.

Please give Ace some feedback