Ranking pairs of masses on a line

Problem

Ranking. Four pairs of masses on a line:

• (A) $m_1 = 1\;\text{kg}$ at $x = 0$, $m_2 = 1\;\text{kg}$ at $x = 1\;\text{m}$;
• (B) $m_1 = 1\;\text{kg}$ at $x = 0$, $m_2 = 3\;\text{kg}$ at $x = 1\;\text{m}$;
• (C) $m_1 = 3\;\text{kg}$ at $x = 0$, $m_2 = 1\;\text{kg}$ at $x = 1\;\text{m}$;
• (D) $m_1 = 2\;\text{kg}$ at $x = 0$, $m_2 = 2\;\text{kg}$ at $x = 3\;\text{m}$.

Rank $x_\text{cm}$ from smallest to largest.

Solution

$x_A = \frac{0 + 1}{2} = 0{,}5 \qquad x_B = \frac{0 + 3}{4} = 0{,}75$ $x_C = \frac{0 + 1}{4} = 0{,}25 \qquad x_D = \frac{0 + 6}{4} = 1{,}5$ Ordering $0{,}25 < 0{,}5 < 0{,}75 < 1{,}5$: $\ev{\text{C} < \text{A} < \text{B} < \text{D}}$

Links

Topics: Centre of mass Concepts: Centre of mass Skills: Calculating the centre of mass · Ranking reasoning