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 center of mass of a uniform plate's position can be found using the formula for a rectangular body's center of mass. For a uniform rectangular plate with dimensions \( a \times b \), the center of mass is at the diagonals' intersection.

Step 2: For a uniform plate, the center of mass coordinates are:

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

where \( a \) and \( b \) are the plate's length and width, and the origin is at a corner.

Step 3: If the origin is not at the plate's center, the center of mass position shifts.

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

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

These are the accurate center of mass coordinates based on the figure's plate dimensions and position.