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The densitis of two solid spheres A and ...

The densitis of two solid spheres A and B of the same radii R very with radial distance `r as p_A(r ) = k ((r )/(R )) and p_B(r ) = k((r )/(R )^5,` respectively, where k is a constant . The moments of inertia of the inividual spheres about axes passing throgh their centres are `I_A and I_B` respectively. if `(I_B)/(I_A) = (n)/(10),` the value of n is

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Moment of inertia of a hollow sphere is `I_(0) = 2/3 mR^(2)`
Here, for sphere A, `I_(A) = int_(0)^( r)2/3r^(2).4pir^(2)dr. Kr/R =(8piK)/(3R) int_(0)^( r)dr -=(8pi K)/(3R).R^(6)/6`
Also, for sphere B: `I_(B) =int_(0)^( r)2/3r^(2).4pir^(2)dr K/R^(5).r^(5) =(8piK)/(3R^(5)).R^(10)/(3R^(5))`, Ratio, `I_(B)/I_(A) = 6/10. rArr n=6`
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