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JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Rotational Mechanics

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Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is , where the value of x is ______.

Answer: 53

Solution

Take the axis perpendicular to the rod through its midpoint. Each sphere has kg, m, and its centre lies m from the axis (half of the 150 cm separation).

By the parallel axis theorem, the moment of inertia of one sphere about the axis is



For both spheres,



So x = 53

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Integer answer

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