Question

At which point is the Centre of gravity situated in a triangular lamina
(A) At the point of intersection of its perpendicular bisector.
(B) At the point of intersection of its angular bisectors.
(C) At the point of intersection of its sides.
(D) At the point of intersection of its medians

Answer 1

Hint: We know that in a triangle median is the point of the centre of mass it means the centre of gravity will be the same in the triangular lamina because we have assumed that the gravity is constant throughout.

Complete step by step answer
It is given in the question that we have to find the centre of gravity situated in a triangle lamina.
We know that the centre of gravity as termed as COG of the at which the combined mass of the body appears to be concentrated, this is a hypothetical point, we can completely describe the motion of any object through space in terms of the transition of the centre of gravity of the object from one place to another, and the rotation of the object about its centre of gravity if it is free to rotate.
In uniform gravity, the centre of mass is the same for the centre of mass of the body. In any regularly shaped body, the centre of mass lies in its centre of that particular body.
We know that in a triangle the point of intersection of the three lines drawn from the vertex to the midpoint of the opposite side is representing the median and it is the centre of the triangle. This intersecting point is also known as the centre of mass of the triangle.
Therefore, the centre of gravity of the triangular lamina is considered at the point of intersection of its median.

Thus, option D is correct.

Additional information
Centre of gravity simplifies our calculation involving gravitational and dynamics to be able to treat the mass of an object we assume as the mass is concentrated at a point. Please note that the centre of gravity is based on weight, whereas the centre of mass is based on mass.

Note:
One can make a mistake by assuming that we cannot find the midpoint of the scalene triangle and thus, it is impossible to predict the Centre of the mass of any random triangle so, we cannot say anything about the centre of gravity of any random triangular lamina.