For the given uniform square lamina ABCD, whose centre is O

Options

A. `sqrt(2I_(AC))= I_(EF)`
B. `I_(AD)= 3I_(EF)`
C. `I_(AC) = I_(EF)`
D. `I_(AC)= sqrt(2I)_(EF)`

Answer

C

Explanation

By the theorem of `bot^(r)` axes-
`I_(Z) + I_(X) + I_(Y) rArr I_(Z)= 2I_(Y)`
[`I_(x)= I_(y)` by the symmetry of the figures]
`I_(EF)= (I_(Z))/(2)`
Now, `I_(Z) = I_(AC) + I_(BD)= 2I_(AC)`
`I_(AC)= (I_(Z))/(2)`
`therefore I_(EF)= I_(AC)`