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Applied Mechanics - Engineering

Q1:

The centre of gravity of a plane lamina will not be at its geometrical centre if it is a

A circle

B equilateral triangle

C rectangle

D square

E right angled triangle.

ANS:E - right angled triangle.

  1. Circle: The center of gravity of a circle coincides with its geometric center. Therefore, the center of gravity will be at the geometric center of a circle.
  2. Equilateral triangle: The center of gravity of an equilateral triangle is at the intersection of its medians. The medians meet at a point called the centroid, which is located one-third of the distance from each vertex along the median. This point may not necessarily coincide with the geometric center for an equilateral triangle.
  3. Rectangle: The center of gravity of a rectangle coincides with its geometric center. Therefore, the center of gravity will be at the geometric center of a rectangle.
  4. Square: A square is a special case of a rectangle, and its center of gravity also coincides with its geometric center.
  5. Right-angled triangle: The center of gravity of a right-angled triangle lies at the intersection of its medians. For a right-angled triangle, the median from the right angle to the hypotenuse (the line from the right angle to the midpoint of the hypotenuse) intersects the hypotenuse at one-third of its length from the right angle. Again, this point may not necessarily coincide with the geometric center for a right-angled triangle.