Two circular loops P and Q are made from a uniform wire. The radii of P and Q are R₁ and R₂ respectively. The moments of inertia about their own axis are I _ P and I _ Q respectively. If I _ P I _ Q = 1 8 then R ₂ R ₁ is

Step-by-step solution

I ₁= M ₁ R ₁^2, I ₂= M ₁ R ₂^2 If m is mas per unit length then aligned & M ₁=2 R ₁ ~m and M ₂=2 R ₂ ~m & M ₁ M ₂ = R ₁ R ₂ & I ₁ I ₂ = M ₁ M ₂ ( R ₁ R ₂ )^2= R ₁ R ₂ ( R ₁ R ₂ )^2= ( R ₁ R ₂ )^3= 1 8 & R ₁ R ₂ = 1 2 or R ₂ R ₁ =2 aligned