Question

A cylinder of given mass and density is constructed tht it's moment of inertia about an axis passing through its com and perpendicular to it's length is the minimum. If the length of the cylinder is root 6. Find radius

Answer 1

as minimum MI of a solid cylinder about its own axis is ½ MR²
and MI about an axis passing through its centre of gravity and perpendicular to its length is
M(L²/12 + R²/4)
½ MR² = M(L²/12 + R²/4)
R²/2 = L²/12 + R²/4
R²/2 – R²/4 = L²/12
L² = 3R²
6=3R^2
R^2=2
R=root2