You make two versions of the same object out of the same material having uniform density. For one version, all the dimensions are exactly twice as great as for the other one. If the same torque acts on both versions, giving the smaller version angular acceleration ?, what will be the angular acceleration of the larger version in terms of ??

Solution 12DQ Step 1: Consider the shape as a uniform sphere. Consider the volume mass density as . Then, the moment of inertia, M 2 I = r dm 0 Where, r - radius of the sphere, dm - elemental mass dm = dV = × r dr2 By, solving the integral we will get, I = MR 2