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Q.

Four persons having masses 10 kg, 20 kg, 30 kg and 40 kg are standing at the corners A, B, C & D respectively of square plank of side 2 m and mass 60 kg. There is no friction between plank and the horizontal surface below it. What is magnitude of displacement of plank when all person meet at the center of plank?

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a

5 cm

b

15 cm

c

25 cm

d

50 cm

answer is C.

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Detailed Solution

Question Image

Center of plank as origin
$\vec{r_{plank, G}} = \frac{10 (\hat{i} - \hat{j}) + 20 (- \hat{i} - \hat{j}) + 30 (- \hat{i} + \hat{j}) + 40 (\hat{i} + \hat{j})}{10 + 20 + 30 + 40 + 60}$
$S$
$S_{p} = - \frac{(m_{1} \vec{S_{1 P}} + m_{2} \vec{S_{2 P}} + m_{3} \vec{S_{3 P}} + m_{4} \vec{S_{4 P}})}{m_{1} + m_{2} + m_{3} + m_{4} + m_{P}} = 0 .25 m .$

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