Question

A machinist starts with three identical square plates, but cuts one corner from one of them, two corners from the second and three corners from the third. Rank the three according to the x-coordinate of their centre of mass, from smallest to largest.

• A. 1, 2, 3
• B. 1, 3, 2
• C. 3, 2, 1
• D. Either a or b

Answer 1

The correct option is D Either a or b

Let the mass of complete square be $M$ and each cut part be $m$.


Taking origin at the centre of complete square.
x coordinate of COM in case [1]:
$x_1=\frac{M\times 0-m\times (-x)}{M-m}=\frac{mx}{M-m}$
In case [2]:
$x_2=\frac{M\times 0-2m\times (-x)}{M-2m}=\frac{2mx}{M-2m}$
In case [3]:
$x_3=\frac{M\times 0-2m\times (-x)-m\times x}{M-3m}=\frac{mx}{M-3m}$

Clearly, $x_1$ is the smallest, but the relation between $x_2$ and $x_3$ is not clear.
So, it can be either $x_1<x_3<x_2$ or $x_1<x_2<x_3$