The gear train shown operates in a horizontal plane and is used to transmit motion to the rack D of mass m_D. If an input torque M is applied to gear A, what will be the resulting acceleration a of the unloaded rack? (The mechanism which it normally drives has been disengaged.) Gear C is keyed to the same shaft as gear B. Gears A, B, and C have pitch diameters d_A, dB, and d_C, and centroidal mass moments of inertia I_A, I_B, and I_C, respectively. All friction is negligible.

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D B. А C.