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Why the centre of gravity coincides with...

Why the centre of gravity coincides with the centre of mass only if the size of the body is small ?

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To understand why the center of gravity (COG) coincides with the center of mass (COM) only if the size of the body is small, we can break down the explanation into several steps: ### Step-by-Step Solution 1. **Definition of Center of Mass (COM)**: - The center of mass of a body is the point where the mass of the body can be considered to be concentrated. It is determined by the distribution of mass within the body. 2. **Definition of Center of Gravity (COG)**: ...
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(1) Centre of gravity (C.G.) of a body is the point at which the weight of the body acts, (2) Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius, (3) To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G.., (4) The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. which one of the following pairs of statements is correct ?

the centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not ,what is the qualitaitve meaning of small and extended in this regard ? for which of the following two coincides ? A building , a pond , a lake ,a mountain ?

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