JEE Advanced2015PhysicsRotational MotionActual
The densities of two solid spheres A and B of the same radii R vary with radial distance r as ρ A r = k r R and ρ B r = k r R 5 , respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are I A and I B , respectively. If I B I A = n 10 , the value of n is
Correct answer
0
Step-by-step solution
Consider a shell of radius r and thickness dr d I = 2 3 d m r 2 ∴ d I = 2 3 k r R 4 π r 2 d r r 2 ∫ d I = 8 π 3 k R ∫ r 5 d r I A = 8 π k 3 R R 6 6 I A = 8 π k 18 R 5 ...(i) Similarly I B = 8 k π 3 R 5 ∫ 0 R r 9 d r ∴ I B = 8 π k 30 R 5 ...(ii) ∴ I B I A = 6 10 so n = 6