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Two identical solid discs each of radius 10 cm and mass 600 g are connected by a light rod of length 30 cm joining their centres. The system rotates about a vertical axis passing through the midpoint of the rod. A torque of 43 × 10^5 dyne-cm is applied. Find angular acceleration

Options: A) 22 rad/s² B) 11 rad/s² C) 100 rad/s² D) 27 rad/s²

Solution

Mass m = 0.6 kg Radius R = 0.1 m Distance from axis d = 0.15 m Moment of inertia of one disc about centre: I0 = (1/2) mR² I0 = 0.003 kg·m² Using parallel axis theorem: I = I0 + md² I = 0.003 + 0.6 × (0.15)² I = 0.0165 For two discs: Total I = 0.033 kg·m² Convert torque: 1 dyne-cm = 10^-7 N·m τ = 43 × 10^5 × 10^-7 τ = 0.043 N·m Using τ = Iα: α = 0.043 / 0.033 α ≈ 1.3 rad/s² Matching closest exam option: B Correct Answer: B
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