From a square sheet of uniform density, a portion is removed shown as shaded region in the figure. Find distance of the centre of mass of the remaining portion from centre of the square if the side of the square is a

Engineering

Physics

Center of Mass

Calculus

Forces and Types of Forces

Question

From a square sheet of uniform density, a portion is removed shown as shaded region in the figure. Find distance of the centre of mass of the remaining portion from centre of the square if the side of the square is a

$\frac{a}{3}$

$\frac{a}{6}$

$\frac{a}{9}$

None of these

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$C_{m} = \frac{a}{2} \times \frac{2}{3} = \frac{a}{3}$

$x_{C} = \frac{M \times 0 - \frac{M}{4} \times \frac{a}{3}}{M - \frac{M}{4}} = \frac{\frac{- Ma}{12}}{\frac{3 M}{4}} = \frac{- a}{9}$ .