The moment of inertia of a uniform circular disc of mass M and of radius R about one of its diameter is

The moment of inertia of a uniform circular disc of mass M and of radi

1.	The moment of inertia of a uniform circular disc of mass M and of radius R about one of its diameter is
Answer» `(1)/(4) MR^(2)` `(1)/(2) MR^(2)` `(2)/(3) MR^(2)` `(2)/(5) MR^(2)` SOLUTION :Moment of INERTIA of the disc about an axis perpendicular to it and through its centre is `(MR^(2))/(2)` x and y axes lie in the plane of the disc and z is perpendicular to it. By the theorem of perpendicular axes, `I_(z) = I_(x) +I_(y)` As x and y axes are along two diameters of the disc . By symmetry, the moment of inertia of the disc is the same about any diameter . Hence `I_(x) = I_(y) "" therefore = I_(z) = 2 I_(x)` `because I_(z) = (1)/(2) MR^(2) "" therefore I_(x) = (I_(z))/(2) = (1)/(4) MR^2` Thus , the moment of inertia of the disc about any of its diameter is `(1)/(4) MR^(2)`.