A uniform square plate of mass 500 g and side length 20 cm rotates about an axis passing through its centre and perpendicular to its plane with an angular speed of 4 rad s ⁻¹ . The moment of inertia of the plate about an axis coinciding with one of its edges is numerically equal to x 10 times its angular momentum about the axis of rotation. The value of x is

Step-by-step solution

The moment of inertia of a uniform square plate about an axis passing through its centre and perpendicular to its plane is I_ = M(a^2 + a^2) 12 = Ma^2 6 The angular momentum about this axis of rotation is L = I_ = ( Ma^2 6 ) 4 = 2 3 Ma^2 The moment of inertia about an axis passing through its centre and parallel to an edge is I_ cm = Ma^2 12 Using the parallel axis theorem, the moment of inertia about one of its edges (which is at a distance of a/2 from the parallel centroidal axis) is I_ edge = I_ cm + M ( a 2 )^2