Two loops P and Q of radii R₁ and R₂ are made from uniform metal wire of same material. I _ P and I _ Q be the moment of inertia of loop P and Q respectively then ratio R₁ / R₂ is ( . Given .I_P / I_Q=27 )

Step-by-step solution

Two loops made from same material I = MR ^2...(i) M = .2 R Substituting in (i), ...( is mass per unit length) aligned & I= 2 R ^3 & I _ P I _ Q = & 2 R ₁^3 2 R ₂^3 & I _ P I _ Q = ( R ₁ R ₂ )^3 & 27 1 = ( R ₁ R ₂ )^3 ( (ii) & R ₁ R ₂ = 3 1 aligned