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Question
The radius of gyration of a body about an axis, at a distance of 0.4 m from its centre of mass is 0.5 m. Find its radius of gyration about a parallel axis passing through its centre of mass.
Solution
Given
`h= 0.4 m`
`K = 0.5 m`
`K_(cm) = ? `
By theorem of parallel axes
`I = I_c+ Mh^2`
`I=MK^2 ` `I_c = MK_(cm)^2`
`MK^2 = MK_(cm)^2+ Mh^2`
`K^2 = K_(cm)^2+h^2`
`(0.5)^2= K_(cm)^2+(0.4)^4`
`K_(cm)^2= (0.5)^2-(0.4)^2`
`=(0.5+0.4)(0.5-0.4)`
`=0.9 xx0.1`
`K_(cm)^2= 0.09`
`K_(cm)= 0.3 m`
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