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Total work of pseudo forces in center of...

Total work of pseudo forces in center of mass frame.
Show that total work done in center of mass frame on all the particles of a system by pseudo forces due to acceleration of mass center is zero.

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Let acceleration of mass centre relative to an inertial is `vec(a)_(c )`. Pseudo force on `I^th` particle of mass `m_i` in center of mass frame is `(-m_(i) vec(a)_(c ))`. Let displacement of Ith particle in a time interval is `Delta vec(r )_(i)` relative to the center of mass frame.
Total work of pseudo forces on all the particles in center of mass frame can now be expressed by the expression
`Sigma(-m_(i) vec(a)_(c )).Delta vec(r )_(i) = -vec(a)_(c).Sigma(m_iDelta vec(r )_(i))=-vec(a)_(c ).vec(0) = 0`
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