First slide

Centre of mass(com)

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 cetre of mass, from smallest to largest.

Moderate

A

3, 1, 2
B

1, 3, 2
C

3, 2, 1
D

1 and 3 tie, then 2

Solution

$\begin{array}{l} x_{1} = (\frac{M (0) - m (- x)}{M - m}) = (\frac{m x}{M - m}) \\ x_{2} = (\frac{M (0) - 2 m (- x)}{M - 2 m}) = (\frac{2 m x}{M - 2 m}) \\ x_{3} = (\frac{M (0) - 2 m (- x) - m (x)}{M - 3 m}) = (\frac{m x}{M - 3 m}) \\ \Rightarrow x_{1} < x_{3} < x_{2} \end{array}$

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