Question

The position of the centre of mass of the uniform plate as shown in the figure is:

• A. \(\left(-\frac{a}{2}, -\frac{b}{2}\right)\)
• B. \(\left(\frac{a}{8}, \frac{b}{8}\right)\)
• C. \(\left(-\frac{b}{6}, -\frac{a}{6}\right)\)
• D. \(\left(-\frac{a}{6}, -\frac{b}{6}\right)\)

Hint:

For a uniform plate, the center of mass lies at the geometric center, and the coordinates are derived by considering the relative dimensions along each axis.

Answer 1

The Correct Option is D

Step 1: The position of the centre of mass of a uniform plate can be calculated by using the formula for the centre of mass of a rectangular body. For a uniform rectangular plate of dimensions \( a \times b \), the centre of mass lies at the intersection of the diagonals.

Step 2: For a uniform plate, the coordinates of the centre of mass are given by:

\[ \left( \frac{a}{2}, \frac{b}{2} \right) \]

where \( a \) and \( b \) are the length and width of the plate, respectively, and the origin is taken at one corner of the plate.

Step 3: If the plate is located such that the origin is at a point shifted from the center of the plate, the position of the centre of mass will be shifted accordingly.

Step 4: The position of the centre of mass relative to the given origin in the figure (assuming a symmetric uniform plate) will be:

\[ \left( -\frac{a}{6}, -\frac{b}{6} \right) \]

This represents the correct coordinates for the centre of mass based on the dimensions and position of the plate in the figure.