Question

The densities of two solid spheres A and B of the same radii R vary with radial distance r as ????ᴀ(r) =
k(r/R) and ????????(r) = (r/R)⁵, respectively, where k is a constant. The moments of inertia of the individual
spheres about axes passing through their centres are Iᴀ and I????, respectively. If I????/Iᴀ = n/10, the value of n is

Answer 1

Answer:

Explanation:

∴Δm=4πx2.Δx.ρ(x)

Moment of Inertia, δI=23(δm)x2

=23×4πx2δxρ(x).x2

or I=∫δI=∫R0234πx4δx.ρ(x)

or we can say that I∝∫R0x4δx.ρ(x)

Using ρA(r)=K(rR) and

ρB(r)=K(r/R)5 and solving,

we get,

IB/IA=610∴n=6

Answer 2

Answer:

option c

Explanation: