Question

How can you find the center of gravity of an Indian map made of steel? Explain.

Answer 1

Centre of gravity is the point on the body at which the force of gravity is concentrated. In simple words this is the point at which the body can be balanced. This could also coincide with centre of mass (especially if the body is symmetrical)

Complete step by step answer:
The centre of gravity is the centre to an object's weight distribution, where the force of gravity can be considered to act. This is the point where the object is perfectly balanced, independent of rotation of the body about the point.
As the map of India is unsymmetrical. So, firstly designate a coordinate system for the map.
Then, find the coordinates of the extreme points of the map with respect to the coordinate system.
Now, let us divide the whole map into sub-parts and find the mass of each part separately. To find the mass, use the formula: $\rho =\dfrac{m}{V}$ . We know the density of steel. Calculate the area of various parts of the map by using the coordinates of extreme points and then multiply the area with the thickness of the map to get the volume. Now, multiply the density of steel and volume of the sub-parts to get the mass.
Now, find the center of mass of each part with the help of a coordinate system (it lies at the center of the object or area).
Now, by using the formula: ${{x}_{cm}}=\dfrac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}$, find the center of mass of the whole map.

Note: In order to answer this question, one must remember the definition of centre of gravity. Also, remember adding the center of mass of additional masses in the formula if available.