Question

As shown in the figure from a uniform rectangular sheet a triangular sheet is removed from one edge. The shift of the centre of mass is

• A. 3.2 cm
• B. 4.2 cm
• C. 5.67 cm
• D. 6.67 cm

Answer 1

The correct option is D 6.67 cm

Mass of plate is uniform, so it can e solved using geometrical method.

Area of triangle, $A_T=\frac{1}{2}\times 30\times 20=300c{m}^2$ A

Area of rectangle, $A_R=20\times 60=1200c{m}^2$

Position of triangle center of mass, $x_T=\frac{2}{3}\times height\frac{2}{3}\times 30=20cm$

$X_{com}=\frac{A_R{x}_R-A_T{x}_T}{A_R-A_T}=\frac{1200\times 0-300\times 20}{1200-300}=-6.67cm$

Center of mass shift is $6.67cm$