Question

Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown.

• A. \( \frac{17}{12} ML^2 \)
• B. \( \frac{13}{12} ML^2 \)
• C. \( \frac{2ML^2}{3} \)
• D. \( \frac{3ML^2}{4} \)

Hint:

When calculating the moment of inertia for a composite system, sum the moments of inertia of individual components, taking into account their distance from the axis of rotation.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
We are asked to find the moment of inertia of a system formed by two identical rods. One rod is vertical and the other is horizontal. The axis of rotation is given as point \( O \).
Step 2: Moment of inertia for vertical rod.
For the vertical rod about \( O \), the moment of inertia is given by: \[ I_1 = \frac{ML^2}{3} \] Step 3: Moment of inertia for horizontal rod.
For the horizontal rod about \( O \), the moment of inertia is: \[ I_2 = \frac{ML^2}{12} + \frac{ML^2}{12} = \frac{ML^2}{6} \] Step 4: Total moment of inertia.
The total moment of inertia of the system is: \[ I_{\text{sys}} = I_1 + I_2 = \frac{ML^2}{3} + \frac{ML^2}{6} = \frac{17}{12} ML^2 \] Step 5: Conclusion.
The moment of inertia of the system is \( \frac{17}{12} ML^2 \), which corresponds to option (1).