A hoop of mass 0.5 kg and radius 2 cm is suspended from a peg at a point on its rim. The moment of inertia about the peg, for an axis perpendicular to the plane of the hoop, is N × 10⁻⁴ kg m². Find N.
Physics · Mixed Chapter
JEE Main Practice

Question

A hoop of mass 0.5 kg and radius 2 cm is suspended from a peg at a point on its rim. The moment of inertia about the peg, for an axis perpendicular to the plane of the hoop, is N × 10⁻⁴ kg m². Find N.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Radius R = 2 cm = 0.02 m; mass M = 0.5 kg. Step 2: About its central perpendicular axis, a thin hoop has I₍CM₎ = MR². Step 3: The peg axis is parallel and a distance R from the centre. By parallel-axis theorem Iₚₑg = I₍CM₎ + MR² = 2MR². Step 4: Iₚₑg = 2 × 0.5 × (0.02)² = 4 × 10⁻⁴ kg m². Final answer: N = 4.