QUESTION: What happens to a body when subjected by a force not passing through center of mass?
If I have a cubical block in free space and if a force is applied at the top surface what will be its motion -will it translate inthe direction of force or it will rotate about com?
And if it rotates about com then why about com and not any other point?
ANSWER: Hello saumil,
The body will be given linear and angular acceleration. The linear acceleration will be a result of a component of the applied force. The line of that component will pass through the com. The other component of your force will be perpendicular to the first and will apply a torque to the body causing angular acceleration about the com.
About your "why about com" question: I haven't been able to put together a better explanation than what I found in these 3 sites.
I especially liked the discussion of spinning while holding a single water bucket.
I hope this helps,
---------- FOLLOW-UP ----------
QUESTION: so if we have force as that in the picture (no force component passing through com)then will their be only angular acceleration about com?
and will the com be at rest?
The image you added changes things. My previous answer applies to the general case. You now specify that the only force has no component passing through com. In that case, the portion of what I said referring to linear acceleration does not apply because the component causing it does not exist. The only acceleration will be angular.
But I caution you: Either the force must only exist for an instant or, as the cube rotates, the direction of the force must change so it continues to have no component passing through the com. (A comment about your figure: There must be a specific point of application of a force. In the case of your figure, it must be in the middle of the upper edge for there to be no component that would pass through the com. Another way to draw that might have the force applied at a corner such that it is perpendicular to a line from the com to the corner.)
I hope this helps,