ABC is a right angled triangular plate of uniform thickness. The sides are such that `AB gt BC` as shown in figure. `I_(1),I_(2) and I_(3)` are moments of inertia about AB,BC and AC respectively. Then, which of the following relation is correct ?

Options

A. `I_(1)=I_(2)=I_(3)`
B. `I_(2) gt I_(1) gt I_(3)`
C. `I_(3) lt I_(2) lt I_(1)`
D. `I_(2) gt I_(1) gt I_(2)`

Answer

B

Explanation

For a given body, mass is same, so it will depend only on the distribution of mass about the axis
The mass is farthest from axis BC, so `I_(2)` is maximum. Mass is nearest to axis AC, so `I_(3)` is minimum.
Hence, the correct sequence will be
`I_(2) gt I_(1) gt I_(3)`