1. The Moon can be taken as a sphere of radius 1740 km with an iron core of uniform density 8000 kg m 3 and a mantle of density 3300 kg m 3 . It is proposed that the core has a radius of 400 km. What is the moment of inertia factor of the Moon for spin about a diameter on the basis of this model? You may assume the result (13.42)

2.A pair of equal spheres of uniform density and each of mass M and radius R are connected by a light rod passing along a diameter of each sphere. The moment of inertia of the system about an axis perpendicular to the rod and passing through its midpoint is 5MR^2 . What is the centre-to-centre distance of the two spheres?

3. A uniform square plate has mass M and side a. What is its moment of inertia (i) about an axis through its centre of mass perpendicular to the plate and (ii) about an axis through one corner perpendicular to the plate?