Two objects are at rest on a level frictionless surface. The objects are not connected. A force `F` is applied to one of the objects, which then moves with acceleration a. Mark the correct statement(s).

Options

A. The concept of centre of mass cannot be applied be-cause the external force does not act on both the objects.
B. The centre of mass moves with acceleration that could be greater than `a`.
C. The centre of mass moves with acceleration that must be equal to `a`.
D. The centre of mass moves with acceleration that must be less than `a`

Answer

D

Explanation

Let the masses be `m_(1)` and `m_(2)`. Then
`F=m_(1)aimpliesa=F/(m_(1))`
`a_(CM)=(m_(1)a+m_(2)xx0)/(m_(1)+m_(2))=F/(m_(1)+m_(2))lta`