Question

The radius of gyration of a body about an axis parallel to axis passing through centre of mass and at a distance 7 cm from centre of mass is

Answer 1

Given that,

Distance = 7 cm

Suppose, center of mass = 5 cm

We need to calculate the radius of gyration

Using formula of center of mass

$I=I_{cm}+Mh^2$

$Mk^2=Mk_{cm}^2+Mh^2$

$k^2=k_{cm}^2+h^2$

Where, k = radius of gyration

h = distance

Put the value into the formula

$0.05^2=k_{cm}^2+0.07^2$

$k_{cm}^2=(0.07)^2-(0.05)^2$

$k_{cm}^2=(0.07-0.05)(0.07+0.05)$

$k_{cm}^2=0.0024$

$k_{cm}=0.04\ m$

$k_{cm} = 4\ cm$

Hence, The radius of gyration is 4 cm.