Question

Mass moment of inertia of a thin rod about its one end is ________ the mass moment of inertia of the same rod about its mid-point.

• A. Same as
• B. Twice
• C. Thrice
• D. Four times

Hint:

When calculating the mass moment of inertia for rods, remember that the distribution of mass relative to the axis of rotation significantly affects the inertia. The farther the mass is from the axis, the larger the inertia.

Answer 1

The Correct Option is C

Recall the mass moment of inertia formulas for a rod. The mass moment of inertia \( I \) of a thin rod about an axis through its midpoint, parallel to the length of the rod, is given by \( \frac{1}{12} ML^2 \) where \( M \) is the mass and \( L \) is the length of the rod. When calculated about one end of the rod, the moment of inertia is \( \frac{1}{3} ML^2 \). Comparing these, \( \frac{1}{3} ML^2 \) is three times \( \frac{1}{12} ML^2 \).