Newton's Second Law in Rotational Form Practice Test

A rigid body with rotational inertia $$I$$ experiences a net torque $$\tau$$, resulting in an angular acceleration $$\alpha$$. If the mass of the body is doubled, with its shape and dimensions remaining identical, what is the new angular acceleration for the same net torque $$\tau$$?

A solid disk and a hoop have the same mass $$M$$ and radius $$R$$. They are both initially at rest and are free to rotate about a fixed, frictionless axle through their centers. The same constant net torque is applied to both. After one second, which of the following correctly compares their angular accelerations, $$\alpha_{disk}$$ and $$\alpha_{hoop}$$?