Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :
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Question

Two small balls with masses m and 2m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is :

Options

G1 Physics · Accepted Answer

Let the distance of mass m from the centre of mass be x. Then the distance of mass 2m from the centre of mass is d - x. Using the centre-of-mass condition, m x = 2m(d - x). Therefore, x = 2d/3, and d - x = d/3. The moment of inertia about the centre-of-mass axis is I = m(2d/3)² + 2m(d/3)² = 4md²/9 + 2md²/9 = 6md²/9 = 2md²/3. Since L = Iω, we have ω = L/I. Therefore, ω = L/(2md²/3) = 3L/(2md²). Correct option: A.