Consider a square ABCD of side 10cm and total mass 10kg. Let O be the center of the sqaure. We cut a square of corners O and C.
Find the central mass of the obtained shape after removing the small cutten sqaure.
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To find the central mass of the obtained shape after removing the small cut square, we need to consider the masses of the remaining parts and their respective distances from the center.
1. Calculate the mass of the large square:
Since the total mass of the square is 10kg and it is distributed evenly, each side of the square has a mass of 2.5kg (10kg/4 sides).
2. Calculate the mass of the cut square:
The cut square has 4 right-angled triangles after removing it. Each triangle is identical and has a quarter of the mass of the large square.
The mass of each triangle is 2.5kg * 1/4 = 0.625kg.
3. Calculate the distance of the large square's center of mass from the center (O):
Since the square is symmetrical, the center of mass coincides with the center of the square. Thus, the distance from O to the center of the large square is zero.
4. Calculate the distance of the cut square's center of mass from the center (O):
Since the cut square has been removed from the large square, its center of mass is irrelevant for the remaining shape. We can consider it to have zero mass and zero distance from the center.
Now we can calculate the central mass of the obtained shape:
Total mass of the remaining shape = mass of the large square - mass of the cut square
= 10kg - (4 * 0.625kg)
= 10kg - 2.5kg
= 7.5kg
Since the cut square has been removed, only the large square remains with a mass of 7.5kg.
Therefore, the central mass of the obtained shape after removing the small cut square is 7.5kg.