Question

the radius of a sphere is 5cm.Calculate the radius of gyration about it's diameter and about any yangent

Answer 1

(i) Radius of gyration about diameter :

Moment of inertia of sphere about diameter is

I = 2/5 (MR^2)
if K(d) is radius of gyration about diameter then,

M x [K(d)]^2 = 2/5 (MR^2)
K(d) = √(2/5) x R

(ii) Radius of gyration about tangent :
 Moment of inertia of sphere about tangent can be calculated by using the theorem of parallel axis

That is

       I = I(d) + MR^2
       I = 2/5 (MR^2) + MR^2
       I = 7/5 (MR^2)
if K(t) is radius of gyration about tangent then,

M[K(t)]^2 = 7/5 (MR^2)
K(t) = √(7/5) x R

i hope it will help you
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