The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are :

Solution

Physics sir · 3 steps

Cut the flag into a tall pole and a small square, then weight each centre by its mass.

1. Split the shape. The pole is the rectangle from (0,0) to (1,3), area 3 m², centre (0.5, 1.5). The flag is the square from (1,2) to (2,3), area 1 m², centre (1.5, 2.5).
2. Masses. The lamina is uniform, so the 4 kg is shared in proportion to area over the total 4 m². The pole has 3 kg and the flag has 1 kg.

   x_(cm) = (3(0.5) + 1(1.5))/4 = 0.75 m, y_(cm) = (3(1.5) + 1(2.5))/4 = 1.75 m

3. So. The centre of mass is at (0.75 m, 1.75 m), option (a).

The idea to keep. For an odd-shaped uniform plate, break it into rectangles, place each mass at its own centre, and take the mass-weighted average. Area stands in for mass.

Answer from the NTA final answer key. Solution by PrepWiser.