Question

The radius of agyration of a body is 18 cm when it is rotating about an axis passing through thecenter of mass of body if radius of gyration of same body is 30 cm about a parallel axis to firstcaxis then paripendicular distance between two parallal axis

Answer 1

Explanation:

As the shape of the body is unknown we assume

I=MR^2

also I=MKa^2 , Ka=18cm

Ka= radius of gyration abt an axis passing through its centre

therefore,

MR^2= MKa^2

R^2=Ka^2

R=Ka=18cm

Kb= radius of gyration abt an axis passing abt a parallel axis = 30cm

I2=MKb^2

By applying parallel axis theorm

MR^2+Mh^2=I2

where 'h' is the perpendicular distance between two parallel axis

M (R^2 + h^2)= M Kb^2

R^2 + h^2= Kb^2

h^2= 30^2 - 18^2

h^2= 576

h= 24 cm