Topic: Engineering Mechanics
The figure shows 3 small spheres that rotate about a vertical axis. The perpendicular distance between the axis and the center of each sphere is given. Mass of highest rotational inertia about that axis, is-
- A. 36
- B. 4
- C. 9
- D. All same
Answer: D. All same
Explanation: Mass of rotational inertia, $I = \text{mass} \times (\text{radius})^{2}$. For the first sphere: $I_{1} = m_{1}r_{1}^{2} = 36 \times (1)^{2} = 36 \text{ kg-m}^{2}$. For the second sphere: $I_{2} = m_{2}r_{2}^{2} = 9 \times (2)^{2} = 36 \text{ kg-m}^{2}$. For the third sphere: $I_{3} = m_{3}r_{3}^{2} = 4 \times (3)^{2} = 36 \text{ kg-m}^{2}$. Since $I_{1} = I_{2} = I_{3}$, all spheres have the same rotational inertia.