Two heavy metallic plates are joined together at 90° to each other. A laminar sheet of mass 30 kg is hinged at the line AB joining the two heavy metallic plates. The hinges are frictionless. The moment of inertia of the laminar sheet about an axis parallel to AB and passing through its centre of mass is 1.2 kg - m 2 . Two rubber obstacles P and Q are fixed, one on each metallic plate at a distance 0.5 m from the line

Step-by-step solution

Let the perpendicular distance of CM from the line AB be r and ω the angular velocity of the sheet just after colliding with rubber obstacle for the first time. Obviously the linear velocity of CM before and after collision will be ν i = r 1 rad / s = r and ν f = r ω . v i → and v f → will be in opposite directions. Now, linear impulse on CM = change in linear momentum of CM or 6 = m ν f + ν i = 30 r + r ω or r 1 + ω = 1 5 ....(i) Similarly, angular impulse about AB = c