The solid cylinder of length 80 cm and mass M has a radius of 20 cm . Calculate the density of the material used if the moment of inertia of the cylinder about an axis C D parallel to A B as shown in figure is 2 . 7 kg m 2 .

Step-by-step solution

I = M r 2 2 + M L 2 4 = ρ π r 2 L r 2 2 + ρ π r 2 L L 2 4 = ρ π r 2 L r 2 2 + L 2 4 ⇒ ρ = I π r 2 L r 2 2 + L 2 4 On putting the values, we get ρ = 1 . 49 × 10 2   kg   m - 3 .