Physics - board, lever

A wooden board weighing 0.5 kg is placed on a table. How much of its length can it protrude over the edge of the table without falling if a weight weighing 0.2 kg is placed at its end?

Correct answer:

r =  5/14

Step-by-step explanation:

$$\begin{gathered} m_1=0.5\text{kg} \\ {m}_2=0.2\text{kg} \\ 0\le r\le 1 \\ {M}_1=M_2 \\ r\cdot L\cdot m_2=(1/2-r)\cdot L\cdot m_1 \\ r\cdot m_2=(1/2-r)\cdot m_1 \\ r\cdot 0.2=(1/2-r)\cdot 0.5 \\ 1.4r=0.5 \\ r=\frac{0.5}{1.4}=0.35714286 \\ r=\frac{5}{14}\doteq 0.357143=\frac{5}{14}=0.3571 \end{gathered}$$

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