Two loops ' A ' and ' B ' of radii ' R₁ ' and ' R₂ ' are made from uniform wire. If moment of inertia of ' A ' is ' I_A ' and that ' B ' is ' B _ B ', then R₂ / R₁ is [ I_A I_B =27 ]

Step-by-step solution

I _ A = M ₁ R ₁^2, I _ B = M ₂ R ₂^2...(i) If m is mass per unit length then M ₁=2 R ₁ ~m and M ₂=2 R ₂ ~m M ₁ M ₂ = R ₁ R ₂ ...(ii) I _ A I _ B = M ₁ M ₂ ( R ₁ R ₂ )^2 [From(i)] I_A I_B == R₁ R₂ ( R₁ R₂ )^2 [From(ii)] I_A I_B = ( R₁ R₂ )^3 array ll 27= ( R₁ R₂ )^3 ( given, , I _A I _ B =27 ) & R ₂ R ₁ = 1 3 array