A square plank of mass m1 = 100 kg and edge length L = 20 \sqrt{2} m is placed on a smooth surface. Two person each of mass m2 = m3 = 50 kg are at corner of a plank as shown in figure. Two person begin to walk on the plank along two different paths as shown in figure and reach nearest corners. What is magnitude of displacement of plank (in m) in the process.

Engineering

Physics

Center of Mass

Question

A square plank of mass m₁ = 100 kg and edge length L = $20 \sqrt{2}$ m is placed on a smooth surface. Two person each of mass m₂ = m₃ = 50 kg are at corner of a plank as shown in figure. Two person begin to walk on the plank along two different paths as shown in figure and reach nearest corners. What is magnitude of displacement of plank (in m) in the process.

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Let displacement of plank be represented by $x \hat{i} + y \hat{j}$
For x-component
50 [L – x ] – 100x – 50x = 0

$x = \frac{L}{4}$

Similarly y-component
50 [L – y ] – 100y – 50y = 0

$y = \frac{L}{4}$

Thus $\vec{r} = - \frac{L}{4} \hat{i} - \frac{L}{4} \hat{j} or | \vec{r} | = \frac{L}{4} \sqrt{2}$

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