The radius of gyration of a body about an axis at a distance of 4 cm from its centre of mass is 5 cm. The radius of gyration about a parallel axis through centre of mass is

Let I_g be the moment of inertia about the centre of the mass of the body. And I₀ be the MI about an axis r m away from the centre of mass.

According to parallel axis theorem,

I₀ = I_g + Mr² ; 

If k_g is radius of gyration at the centre of mass , k₀ is radius of gyration at r =4cm, then

Mk₀² = Mk_g² + Mr² 

k₀² = k_g² + r² 

$\Rightarrow$5 = k_g² +4² 

$\Rightarrow$k_g = 3 cm