A square lamina has I = 20 kg·m² about the central perpendicular axis. Find its moment of inertia about an axis along an edge (kg·m²).
Physics · Mixed Chapter
JEE Main Practice

Question

A square lamina has I = 20 kg·m² about the central perpendicular axis. Find its moment of inertia about an axis along an edge (kg·m²).

G1 Physics · Accepted Answer

Step 1: For a square, the central perpendicular-axis moment is Iᶻ = ma²/6 = 20. Step 2: About a central axis in its plane and parallel to the edge, Iₓ = ma²/12 = 10. Step 3: Shift the axis from centre to edge using d = a/2: Iedge = Iₓ + m(a/2)² = ma²/3. Step 4: Since ma²/6 = 20, Iedge = 2×20 = 40 kg·m².