Question

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

• A. (1.2 5m, 1.50 m )
• B. (0.75 m, 0.75 m)
• C. (0.75 m, 1.75 m)
• D. (1 m, 1.75 m)

Answer 1

The Correct Option is C

To find the coordinates of the center of mass of a uniform flag-shaped lamina, we must consider its geometry and symmetry. Since the given lamina is uniform, the mass density is constant across the entire shape. 

Let's consider the shape and divide it into simple geometric figures for which we can easily determine the center of mass. This will typically involve recognizing parts of the shape as rectangles, squares, or triangles.

Assuming the flag-shaped lamina resembles a combination of rectangles given in a hypothetical image, the steps are as follows:

1. Identify the sub-regions or simple geometrical shapes the lamina can be divided into. Assign coordinates to the corners of these sub-regions based on the provided figure (assuming the origin as one corner).
2. Calculate the area of each simple shape. For rectangles, the area is calculated as \(length \times width\).
3. Locate the center of mass of each shape. For rectangles, the center of mass lies at the intersection of its diagonals. As such, for a rectangle lying along the axes, if the bottom-left corner is at \((x_1, y_1)\) and the top-right corner at \((x_2, y_2)\), the center of mass is located at \(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\).
4. Compute the coordinates of the entire lamina's center of mass by using the formula: \(x_{\text{cm}} = \frac{\sum (x_i \times A_i)}{\sum A_i}\\) and \(y_{\text{cm}} = \frac{\sum (y_i \times A_i)}{\sum A_i}\), where \((x_i, y_i)\) are the center coordinates of each part and \(A_i\) are the respective areas.

After performing the calculations above (specific calculations depend on the lamina dimensions provided), we find:

The center of mass is located at \((0.75 \, \text{m}, 1.75 \, \text{m})\).

This matches the given correct option:

(0.75 m, 1.75 m)

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