Question

The moment of inertia of a uniform rod of mass 0.50 kg and length 1 m is 0.10 kg-m² about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.

Answer 1

Length of the rod = 1 m, mass of the rod = 0.5 kg
Let at a distance d from the center the rod is moving
Applying parallel axis theorem :
The moment of inertial about that point
(mL² / 12) + md² = 0.10
(0.5 × 1²)/12 + 0.5 × d² = 0.10
d² = 0.2 – 0.082 = 0.118
d = 0.342 m from the centre.