Two solid spheres (A and B) are made of metals having densities _A and _B respectively. If there masses are equal then ratio of their moments of inertia ( I_B I_A ) about their respective diameter is

Step-by-step solution

Mass = Volume Density Mass of spheres A and B is, M _ A = 4 3 R _ A ^3 _ A and M _ B = 4 3 R _ B ^3 _ B If masses are equal, M _ A = M _ B 4 3 R _ A ^3 _ A = 4 3 R _ B ^3 _ B R_B R_A = ( _A _B )^ 1 3 Moment of inertia of sphere about its diameter is given by, I = 2 5 MR ^2 array ll & I_A= 2 5 M_A R_A^2 and I_B= 2 5 M_B R_B^2 & I_B I_A = R_B^2 R_A^2 array I_B I_A = ( _A _B )^ 2 3 [ From (i) ]