An equilateral triangle ABC is cut from a thin solid sheet of wood .(see figure ) D,E and F are the mid-points of its sides as shown and G is the centre of the triangle.The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane to the triangle is `I_(0)` If the smaller triangle DEF is removed from ABC , the moment of inertia of the remaining figure about the same axis is I. Then :

Options

A. `I=9/16 I_(0)`
B. `I=15/16 I_(0)`
C. `I=3/4 I_(0)`
D. `I=I_(0)/4`

Answer

B

Explanation

Since, moment of inertial is proportional to square of side length and base I of `triangleDEF` about its centroid will be `1/4`th because of side length because of mass. So `I(DEF) = I_(0)/16`.
So, for the remaining portion, `I=I_(0)- I_(0)/4 = (15 I_(0))/16`