Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Options

A. `73/2 MR^(2)`
B. `181/2 MR^(2)`
C. `19/2 MR^(2)`
D. `55/2 MR^(2)`

Answer

B

Explanation

`I_(0) = (MR^(2))/2 + 6[(MR^(2))/2 + M(2R)^(2)] =MR^(2) [1/2 + 3 + 24]=55/2 MR^(2)`
O is the centre of mass of the system. Applying parallel axis theorem between O & P.
`I_(P) = I_(0) + 7M(3R^(2)) = 55/2 MR^(2) + 63 MR^(2) = 181/2 MR^(2)`