A uniformly thick plate in the shape of an arrow head has dimensions as shown. Find the distance of centre of mass from point `O` (in cm)

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

A

Explanation

Ans.(1)
Note that the centre of mass of a uniform thick triangular sheet is at the centroid which divides a medium in a ratio `2:1`. The required centre of mass must be on the line of symmetry passing through `O` and the vertex to the right . Consider the shape of arrowhead to be obtained by cuting the triangular part to the left (with base `6 cm` and height `3cm`) from the uncut triangular sheet with base `6cm` and height `9cm`. The ratio of masses of these two is `3:1` the thickness being uniform.
`X_(CM)=(m_(2)x_(2)-m_(1)x_(1))/(m_(2)-m_(1))=-1cmrArr` right of `O`