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

Options

A. `I_(0) +ML^(2)//2`
B. `I_(0) + ML^(2)//4`
C. `I_(0) + 2ML^(2)`
D. `I_(0) + ML^(2)`

Answer

B

Explanation

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)`