Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torque between two discs is 43 × 10⁵ dyne cm, the angular acceleration of the discs about the given axis AB i $s ______$ rad/s².

Question

G1 Physics · Accepted Answer

Let m = 600 g = 0.6 kg, R = 10 cm = 0.10 m. The rod length is 30 cm = 3R. From the figure, the axis AB is at distance R from the centre of the left disc and 2R from the centre of the right disc. For a thin disc, the moment of inertia about a diameter through its centre is I(disc,CM) = mR²/4. Therefore, for the left disc, I₁ = mR²/4 + mR² = 5mR²/4. For the right disc, I₂ = mR²/4 + m(2R)² = 17mR²/4. For the rod, I(rod,CM) = m(3R)²/12 = 3mR²/4. The rod centre is at distance R/2 from axis AB, so I(…