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A **disc** of mass $M$, radius $R$ rolls without slipping. A particle of mass $m$ rests on its **top** (sticks). Effective moment of inertia of the system about the instantaneous axis of rotation (line of contact) is:
A$\tfrac{3}{2}MR^2 + 4mR^2$
B$\tfrac{3}{2}MR^2 + 2mR^2$
C$\tfrac{1}{2}MR^2 + mR^2$
D$MR^2 + 2mR^2$
Answer & Solution
Correct answer: A. $\tfrac{3}{2}MR^2 + 4mR^2$
Disc about contact (parallel axis): $\tfrac{1}{2}MR^2 + MR^2 = \tfrac{3}{2}MR^2$. Particle is at distance $2R$ from contact (vertical chord through top): $I_p = m(2R)^2 = 4mR^2$. Total: $\tfrac{3}{2}MR^2 + 4mR^2$.
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