Question

A proton and an electron, initially at rest, are allowed to move under their mutual attractive force. The center of mass will:

Answer 1

Hint: Center of mass of the body is that hypothetical point where we have assumed the whole mass of the given body is present or concentrated; it can even lay outside the boundaries of a specific body. To find the center of mass of bodies we multiply the masses with their positions and divide the whole term by addition of all masses.

Complete answer:
When we take a body mass concentrated at a point which we call as center of mass it becomes easier for us to solve problems. When a system of bodies experiences an external force then only the center of mass of the system changes and follows Newton’s second law to trace out its trajectory. The acceleration of center of mass due to presence of external force on system is given by:
\[F = ma\]

Protons and electrons move towards each other due to an internal force i.e. the mutual attraction force acting between them and hence the center of mass does not change. It remains at the same position when the system is at rest.

Note: The same happens when a body explodes in its path. As this happens due to the internal forces the center of mass of the body follows the same trajectory that it would have followed when mass does not explode. Center of mass of two bodies, one having greater mass is slightly located near the heavier body.