The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

The moment of inertia of a thin uniform rod of mass M and length L abo

1.	The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
Answer» `I_(0) +ML^(2)//2` `I_(0) + ML^(2)//4` `I_(0)+ 2ML^(2)` `I_(0) + ML^(2)` Solution :According to the theorem of parallel axes , the moment of inertia of the THIN rod of MASS M and length L about an axis passing through one of the ends is `I = I_(CM) + Md^2` where `I_(CM)` is the moment of inertia of the given rod about an axis passing through its centre of mass and perpendicular to its length and d is the distance between TWO parallel axes. Here `I_(CM) = I_(0) , d = (L)/(2) therefore I = I_(0) + M ((L)/(2))^(2) = I_(0) + (ML^(2))/(4)`