A uniform rod of length 1 metre has a mass of `500 gram`. What is moment of inertia of the rod about an axis passing through the centre of the rod perpendicular to its length. How is moment of inertia changed when the same axis passes through one end of the rod ?

Explanation

Here, `l = 1m, M = 500 g = (1)/(2)kg`
About an axis passing through the centre of the rod and perpendicular to its length,
`I = M(l^(2))/(12) = (1)/(2) xx (1^(2))/(12) = (1)/(24) kg m^(2)`
When same axis passes through one end of the
rod, `x = (l)/(2) = (1)/(2) m`,
applying theorem of parallel axes,
`I' = I + Mx^(2)`
`I' = (1)/(24) + (1)/(2).((1)/(2))^(2) = (1)/(24) + (1)/(8) = (1)/(6)kg m^(2)`