question_answer

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

A) 3, 1, 2  

B) 1, 3, 2

C) 3, 2, 1 

D) 1 and 3 tie, then 2

Correct Answer: B

Solution :

[b] \[{{x}_{1}}=\left. \left( \frac{mx}{M-m} \right) \right|{{x}_{2}}=\left. \left( \frac{2mx}{M-2m} \right) \right|{{x}_{3}}=\left( \frac{mx}{M-3m} \right)\] \[{{x}_{1}}<{{x}_{3}}<{{x}_{2}}\]