Consider the following necessary and sufficient conditions for replacing a rigid body by a dynamical equivalent system of two masses:

1). Total mass must be equal to that of the rigid body 2). Sum of the squares of radii of gyration of two masses about the c.g. of the rigid body must be equal to square of its radius of gyration about the same point 3). The c.g. of two masses must coincide with that of the rigid body 4). The total moment of inertia of two masses about an axis through the c.g. must be equal to that of the rigid body Which of the above conditions are correct?

(a) 1,2 , and 3

(b) 1,3 , and 4

(c) 2,3 , and 4

(d) 1,2 , and 4 .