Angular velocity of a solid sphere from angular momentum

Practice question

Question

A solid sphere of mass 2kg and radius 0.1m has an angular momentum of 4kg m2/s about its axis. What is its angular velocity?

Options

Choose one · Correct answer highlighted

400 rad/s 450 rad/s 500 rad/s Correct 550 rad/s

Explanation

L = Iω. For a sphere: I = 25MR2 = 25×2×(0.1)2 = 0.008kg m2. ω = LI = 40.008 = 500rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 500 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

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