We know that point is something which has no dimension ( length, breadth etc.) but has existence. As point has no dimension, it has no volume. Moreover, it has no mass.

Density(d) = Mass(m) / Volume(v) m = d * v m = 0 ( since v = 0 )

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But we are given problems such as - “ A point mass of 5 kg is moving with velocity …” . Are these problems composed in right manner ? Is it possible for a point to have mass greater than 0 ?
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TopNewestin modern approach of geometry(started by hilbert)we actually dont define the fundamental geometric objects such as points or lines.rather we study the inter relationships of these objects(betweenness,on ness).but d=v/m is a physical formulation.you can discuss a classic book the 'foundation of geometry' by david hilbert

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Just study the concept of center of mass and everything will become clear. And oh, yes, point masses have a new notion when you go into the quantum world.

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When a body undergoes non rotational motion due to the forces action on it, we can consider the body as a point object...In translational motion, all points in the body have same displacement, velocity, and acceleration..(by same i mean they are all equal and in same direction.) So, we model the body to be a point where all the mass is concentrated... On the contrary, in rotational motion, different point in the body have different displacements, velocities, and accelerations.... So, we can't consider the body as a particle...

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