A square plate has a diagonal of length 21 cm. One of it’s corner is cut along the line joining the midpoint of neighbouring two sides. How far is new centre of mass from original centre of mass?

Engineering

Physics

Center of Mass

Question

none of these

1.75 cm

0.25 cm

1.25 cm

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$a^{2} \times σ \times 0 + \frac{1}{2} \frac{a}{\sqrt{2}} \times \frac{a (- σ)}{2 \sqrt{2}} \times \frac{\sqrt{2} a}{3}$

$a^{2} σ - \frac{a^{2} σ}{8}$

$a^{2} σ \times 0 - \frac{a^{2} σ}{8} \times \frac{- \sqrt{2} a}{3}$

$a^{2} σ - \frac{a^{2} σ}{8}$

$= - \frac{\sqrt{2} a}{8 \times 3} \div (\frac{8 - 1}{8}) = - \frac{\sqrt{2} a}{21} (a = \frac{21}{\sqrt{2}})$

= – 1 cm

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