Center of MassHardBloom L3
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 plates according to the x-coordinate of their centers of mass, from smallest to largest.
Options
A.3, 1, 2
B.1, 3, 2
C.3, 2, 1
D.1 and 3 tie, then 2
Solution
Sol. 
$x_{cm_{1}} = \frac{M \times 0 - m( - x_{0})}{M - m} = \left( \frac{mx_{0}}{M - m} \right) = \frac{x_{0}}{\frac{M}{m} - 1}$
$x_{cm_{2}} = \frac{M \times 0 - m( - x_{0}) - m_{0}( - x_{0})}{M - 2m_{0}}$
$x_{cm_{2}} = \frac{2mx_{0}}{(M - 2m)} = \frac{x_{0}}{\frac{M}{2m} - 1}$
$x_{cm_{3}} = \frac{Mx_{0} - m( - x_{0}) - m( - x_{0}) - {mx}_{0}}{M - 8m} = \left( \frac{mx_{0}}{M - 3m} \right) = \frac{x_{0}}{\frac{M}{m} - 3}$
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