You can use plumb lines to find its center of gravity.
Hold it from one point and draw vertical line in direction of gravity (plumb line). Hold it from another point and do the same, and a third point if necessary; where the lines cross is center of gravity
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Mass divided by Volume = Density. Or use the displacement method for an irregularly shaped object.
It is the displacement method.
Google "Archimedes' Principle" and see if that gives you a clue...
Half fill a graduated glass beaker with water and note the level. Place irregularly shaped object into the beaker. Note the new level. The difference between the two levels is the volume of the object. cw: OK, that method works for objects that don't get wet -- like steel. Tissue paper would not be a good candidate. Also, if the object floats, you have to submerge the object.
Finding the center of gravity of an irregularly shaped object can be done using the plumb line method.
You can locate the center of gravity of irregularly shaped objects by using the plumb line method, which involves suspending the object and letting it come to rest naturally. Another method is to use physical calculations based on the object's mass distribution to determine the center of gravity. Computer simulations can also be used to estimate the center of gravity for complex shapes.
An object's center of gravity always lies at the point where its weight can be considered to act. For a symmetrical object like a sphere, the center of gravity is at its geometric center. In irregularly shaped objects, the center of gravity may not necessarily be located at the geometric center.
No, the center of gravity of an irregularly shaped object does not have to be located inside the object. The center of gravity is the point where the weight of the object is concentrated, and it can be located both inside and outside the object depending on its shape and distribution of mass.
Secret
The center of gravity using the plumb line method is determined by suspending an object from different points and allowing it to come to rest. The intersection of the lines traced by the plumb bob at each resting position indicates the center of gravity of the object. This method is commonly used to locate the center of gravity of irregularly shaped objects or structures.
The center of gravity plumbline method involves suspending an object to find its center of gravity by allowing it to hang freely and marking the line of plumb underneath it. The intersection of the plumb lines from two or more positions will determine the center of gravity. This method is commonly used in physics and engineering to locate the balance point of irregularly shaped objects.
The intersection of the three lines represents the point where the lamina would balance perfectly if placed on a pin. This point is the center of gravity because it is the average position of all the mass in the lamina, considering both their magnitude and distribution. The center of gravity is a key concept in physics to understand the equilibrium and stability of an object.
the water displacement method
You can find the volume of an irregularly shaped object, like a rock, by using the water displacement method. Submerge the object in a known volume of water in a container. Measure the increase in water level, which equals the volume of the rock.
Mass divided by Volume = Density. Or use the displacement method for an irregularly shaped object.
What you are asking is quite clear, but the wording is a little misleading. Every object containing any amount of mass, however great or small, has gravity. So the answer to your question will essentially be the answer for any massive body whether it is a planet or a bowling ball. Gravity is a property of mass. Since every little bit of the planet earth is exerting its gravitational effect on you, then there must be a place within the earth that is the point where all the individual effects 'average out'. That point is the 'center of gravity'. If you mentally take any solid object that is irregularly shaped (but not too strangely shaped for a first go at this) then you can do the following. Suspend the object from a point on the surface and notice how the object settles. Imagine a perfectly straight line going down through the object from the point of suspension to the earth's center of gravity. Now choose any other suspension point for the object and do it again. The two 'lines' formed in the object will meet at one point. No matter how many times you suspend the object freely from a point on its surface, the lines going down through the object will all meet at one point-- the object's center of gravity. [With very irregularly shaped objects, this point might even be outside of the object itself!] If you could somehow suspend the object perfectly on a tiny ball bearing right at that point, the object would move and turn freely, without any part of the object tending to settle toward earth. The center of gravity would be a perfect balance point for the object. Because planets and moons are naturally formed, their materials are not perfectly smoothely distributed within them. So centers of gravity are usually not the very same point as the 'geometric center'. The same is true for a black hole. It may even be simpler for black holes. The singularity, the center of gravity and the 'geometric center', whatever that means for black holes, would probably always be the same point.