Two identical solid spheres each of mass 2 kg and radius 10 cm are fixed at the ends of a light rod. The separation between their centres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod through its midpoint is ______ × 10⁻³ kg m².
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 1 Morning Shift

Question

Two identical solid spheres each of mass 2 kg and radius 10 cm are fixed at the ends of a light rod. The separation between their centres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod through its midpoint is ______ × 10⁻³ kg m².

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

For each solid sphere about the system's central axis, use the parallel-axis theorem. Mass of each sphere: m = 2 kg Radius: R = 0.10 m Distance of each sphere's centre from the midpoint: d = 0.20 m Moment of inertia of one sphere: I₁ = (2/5)mR² + md² = (2/5)(2)(0.10)² + 2(0.20)² = 0.008 + 0.080 = 0.088 kg m² For two spheres: I = 2×0.088 = 0.176 kg m² = 176×10⁻³ kg m² Final value: 176