Moment of inertia of a disc of radius R about a diametric axis is 25 ~kg ~m ^2 . The moment of inertia of the disc about a parallel axis at a distance R / 2 from the centre is

Step-by-step solution

From the perpendicular axis theorem, we have I_z=I_x+I_y where, I_z is moment of inertia about Z-axis, I_x is moment of inertia about X -axis and I_y is moment of inertia about Y -axis. Moment of inertia of a disc, I_z= 1 2 M R^2 Now, I_x=I_y , because two perpendicular diameters are equivalent. aligned & So, I_ diameter = 1 2 1 2 M R^2= M R^2 4 & M R^2 4 =25 (given) & M= 100 R^2 ~kg aligned Also every diameter passes through centre of mass. So, I_ COM = M R^2 4 =25 ~kg - m ^2 Using parallel axis theorem, aligned I