Question

The radius of gyration of a uniform rod of length `l`, about an axis passing through a point `l/4` away from the centre of the rod, and perpendicular to it, is: ____________.

Options

• `1/8l`

• `sqrt(7/48)l`

• `sqrt(3/8)l`

• `1/4l`

Answer 1

The radius of gyration of a uniform rod of length `l`, about an axis passing through a point `l/4` away from the centre of the rod, and perpendicular to it, is: `sqrt(7/48)l`.

Explanation:

`"I"_0 = "I"_e + "Mh"^2`

`= ("M"l^2)/12 + m(l/4)^2`

` = ("M"l^2)/12 + ("M"l^2)/16`

`therefore "I"_0 = (7"M"l^2)/48`

`"but K"  sqrt("I"/"M") = sqrt((7"M"l^2)/(48"M"))`

`therefore  "K" = sqrt(7/48)l`