A uniform rigid body of circular cross-section (mass m , radius R ) is rolling without slipping on a horizontal flat surface. The magnitude of its total angular momentum about a point on the surface in its path is 7 5 times the magnitude of its translational angular momentum about the same point. The shape of the body is

Step-by-step solution

Let the moment of inertia of the body about its center of mass be I_ cm . For a body rolling without slipping with center of mass velocity v , its angular velocity is = v R . The translational angular momentum of the body about a point on the surface is: L_ trans = m v R = m ( R) R = m R^2 The total angular momentum about the same point is the sum of translational and rotational angular momenta: L_ total = L_ trans + L_ rot = m v R + I_ cm = m R^2 + I_ cm According to the given condition: L_ total = 7 5 L_ trans Su