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 linear speeds of a point on the rim of A and a point on the rim of B are v_A and v_B respectively. We have

Step-by-step solution

Mass of disc A is m_A = r^2 t Mass of disc B is m_B = (4r)^2 ( t 4 ) = 4 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 _A = I_A and _B = I_B = 64 I_A = _A 64 At a later instant t₀ , the angular speeds are _A = _A t₀ and _B = _B t₀ = _A 64 The linear speeds of points on the rims are v_A = _A r and v_B = _B (4r) = ( _A 64 ) (4r) = _A r 16 = v_A 16 The