Three rings, each of mass P and radius Q are arranged as shown in the figure. The moment of inertia of the arrangement about YY' axis will be

Options

A. `7/2 PQ^(2)`
B. `2/7 PQ^(2)`
C. `2/5 PQ^(2)`
D. `5/2 PQ^(2)`

Answer

A

Explanation

For ring 1 and 2 using parallel axis theorem,
`I_(1) = I_(2) = I_(cm) + Md^(2)`
`I_(1) = I_(2) = 3/2 PQ^(2)`
For ring 3,
`I_(3) = 1/2 PQ^(2)`
Moment of inertia of the arrangement,
`I = I_(1) + I_(2) + I_(3)`
`I = 3/2PQ^(2) + 3/2 PQ^(2) + 1/2 PQ^(2)`
`I = 7/2 PQ^(2)`