Two circular discs A and B are made of the same material. Disc A has radius r and thickness t , while disc B has radius 4r and thickness t/4 . Equal torques act on both discs, initially at rest. At a later instant, the

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Correct answer: A. v_A > v_B

Mass of disc A is m_A = π r^2 t Mass of disc B is m_B = π (4r)^2 ((t)/(4)) = 4 π r^2 t = 4m_A Moment of inertia of disc A is I_A = (1)/(2) m_A r^2 Moment of inertia of disc B is I_B = (1)/(2) m_B (4r)^2 = (1)/(2) (4m_A) (16r^2) = 64 I_A Since equal torques act on both discs, their angular accelerations are α_A = ( )/(I_A) and α_B = ( )/(I_B) = ( )/(64 I_A) = (α_A)/(64) At a later instant t_0 , the angular speeds are ω_A = α_A t_0 and ω_B = α_B t_0 = (ω_A)/(64) The linear speeds of points on the rims are v_A = ω_A r and v_B = ω_B (4r) = ((ω_A)/(64)) (4r) = (ω_A r)/(16) = (v_A)/(16) Therefore, v_A > v_B Answer: v_A > v_B

Two circular discs A and B are made of the same material. Disc A...

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