A uniform square lamina has side a and mass m. Express moment of inertia about an axis through a corner perpendicular to its plane as kma². Find k (to two decimals).
Physics · Mixed Chapter
JEE Main Practice

Question

A uniform square lamina has side a and mass m. Express moment of inertia about an axis through a corner perpendicular to its plane as kma². Find k (to two decimals).

G1 Physics · Accepted Answer

Step 1: Through the centre and perpendicular to plane, Icm = (1/6)ma². Step 2: Distance from centre to corner is d = a/√2. Step 3: Apply parallel-axis theorem Icorner = Icm + md² = ma²(1/6+1/2) = (2/3)ma². Step 4: k = 2/3 ≈ 0.67.