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. (Assuming that the side of each square removed is less then the half of the side of the square plate)

• 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]:
$x_1=\frac{M\times 0-m\times (-a)}{M-m}=\frac{ma}{M-m}$
In case [2]:
$x_2=\frac{M\times 0-2m\times (-a)}{M-2m}=\frac{2ma}{M-2m}$
In case [3]:
$x_3=\frac{M\times 0-2m\times (-a)-m\times a}{M-3m}=\frac{ma}{M-3m}$
From the given conditions we can say that,
$x_1<x_3<x_2$