A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass the same. Which of the following physical quantities would remain constant for the sphere?

In free space, no external torque is acting on the sphere. If the mass remains constant and the radius is increased, then the moment of inertia, rotational kinetic energy, and angular velocity will change. However, according to the law of conservation of angular momentum, the angular momentum will remain constant. Angular momentum (L) is given by L = Iω, where I is the moment of inertia and ω is the angular velocity. Since no external torque acts, the angular momentum remains conserved. When the radius increases, the moment of inertia (I) increases (I is proportional to R², where R is the radius for a solid sphere). To conserve angular momentum, the angular velocity (ω) must decrease proportionally.