Question

The objects and the corresponding positions of centre of mass are given below. The FALSE one is

• A. Uniform rod : middle point of the rod
• B. Circular ring: centre of the ring
• C. Triangular lamina : point of intersection of altitudes
• D. Cylinder: middle point on its axis
• E. Cubical box: intersection of diagonals

Hint:

Logic Tip: In geometry, altitudes meet at the Orthocenter, angle bisectors meet at the Incenter, perpendicular bisectors meet at the Circumcenter, and medians meet at the Centroid. Mass distribution always balances around the Centroid!

Answer 1

The Correct Option is C

Concept:
The center of mass of a uniform geometric object typically lies at its geometric center (centroid). We must evaluate each object to find the incorrect pairing.
Step 1: Evaluate the symmetric objects.
For regular, uniform, symmetrical bodies, the center of mass always coincides with the geometric center. - Uniform rod: Geometric center is the midpoint. (True) - Circular ring: Geometric center is the center of the circle. (True) - Cylinder: Geometric center is the midpoint of the central axis. (True) - Cubical box: Geometric center is the intersection of the body diagonals. (True)
Step 2: Evaluate the triangular lamina.
A uniform triangular lamina is a 2D flat triangle. Its center of mass is located at its geometric centroid. The centroid of a triangle is mathematically defined as the point of intersection of its medians (the lines connecting each vertex to the midpoint of the opposite side). The option claims it is the intersection of \textit{altitudes} (the orthocenter), which is incorrect.