A laminar sheet of mass 30 kg is hinged along AB between two perpendicular heavy plates. Its moment of inertia about an axis through its centre of mass parallel to AB is 1.2 kg·m². Obstacles P and Q are each 0.5 m from AB. The sheet hits an obstacle with angular speed 1 rad/s, reverses, and receives impulse 6 N·s at each impact. Which option correctly gives (i) CM distance from AB, (ii) angular speed after the first impact, and (iii) whether it ever comes to rest?

Question

G1 Physics · Accepted Answer

Let d be the distance of the lamina CM from hinge AB. Zero hinge reaction during impact means the linear impulse condition J=mΔV of CM is consistent with angular impulse J(0.5)=IₐBΔω, where IₐB=I about CM+md². Using J=6 N·s, m=30 kg and I about CM=1.2 kg·m² gives d=0.1 m. The impact reverses the sheet with angular speed 1 rad/s; with the given perfectly repeating impulse geometry, it never comes to rest. Hence option B.