The radius of gyration of a sphere of mass M and radius R about the axis parallel to the axis passing through its centre and tangent to the sphere is

Options

A. `(7)/(5)R`
B. `(3)/(5)R`
C. `(sqrt((7)/(5)))R`
D. `(sqrt((3)/(5)))R`

Answer

(c)

Explanation

Radius of gyration of sphere about an axis passing through centre is,
`I=(2)/(5)MR^(2)`
From parallel axis theorem, moment of inertia of sphere about any axis is,
`I=I_(0)+MR^(2)`
`I=(2)/(5)MR^(2)+MR^(2)= (7)/(5)MR^(2)`
`I=Mk^(2)`, where 'k' is the radius of gyration (Given)
`Mk^(2)=(7)/(5)MR^(2)`
`k^(2)=(7)/(5)R^(2)`
`k=sqrt((7)/(5))R`