Seven identical coins are rigidly arranged on a flat table in the pattern shown below so that each coin touches its neighbors. Each coin is a thin disc of mass m and radius r. Note that the moment of inertia of an individual coin about an axis passing through centre and perpendicular to the plane of the coin is `m^(2)//2`

The moment of inertia of the system of seven coins about an axis that passes through the point P (the centre of the coin positioned directly to the right of the central coin) and perpendicular to the plane of the coins is–

Options

A. `(55)/(2)mr^(2)`
B. `(127)/(2)mr^(2)`
C. `(111)/(2)mr^(2)`
D. `55mr^(2)`

Answer

C

Explanation

`I_(p)=(mr^(2))/(2)+3[(mr^(2))/(2)+m(2r)^(2)]+[(mr^(2))/(2)+m(r2sqrt(3))^(2)]`

`xx2+[(mr^(2))/(2)+(4r)^(2)m]`
`=(111)/(2)mr^(2)`