Question

The ratio of moment of inertia of two solid sphere of same mass but densities in the ratio 1:8 is ​

Answer 1

Explanation:

Let the density of sphere be ρ and 8ρ

Since there mass =m is same so ,

3

4πr

a

3

ρ

=

3

4πr

b

3

8ρ

So r

a

=2r

b

I

b

I

a

=

r

b

2

r

a

2

=4:1

hope this will help and support

Answer 2

Answer:

Let M1 and M2 be the masses of two solid spheres of densities d1 and d2.  

According to your problem , M1 = M2  

M = 4/3πR³ X d  

so , 4/3πR1³ X d1 = 4/3πR2³ X d2  

= (R1/R2)³ = d1/d2 = 8/1  

R1/R2 = 2/1.  

The ratio of moments of inertia of the spheres ,  

(R1/R2)² = (2/1)²  

= 4/1