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# Block with a force

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BLOCK WITH A FORCE

THERE IS A BLOCK OF SIDE X METRES RESTING ON A FRICTIONLESS SURFACE

A FORCE F IS APPLIED AT THE LEFT TOP OF THE BOX(TAKE THE DIRECTION OF FORCE IS FROM LEFT TO RIGHT) HORIZONTALLY

NOTE: THE FORCE IS NOT AT THE CENTRE OF GRAVITY.

PROVE THAT THE BOX TENDS TO ROTATE ABOUT THE CENTRE OF GRAVITY ONLY.

ALSO PROVE THAT THE BOX WILL NOT TEND TO ROTATE ABOUT ANY OTHER POINT EXCEPT THE CENTRE OF GRAVITY.

https://brainmass.com/physics/gravity/box-tend-rotate-center-gravity-50605

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Before the force F is applied, the only force acting upon the box are
(a) the weight of the box acting vertically downwards through its centre of gravity and
(b) the reaction of the frictionless surface.
The reaction of the surface is the resultant of the total reactions of the several points of contact of the box
with the surface and it acts through a point inside the base.

Since the box is at rest before the force F is applied, the weight of the box and the reaction of the
surface must be equal and opposite and also have the same line of action.

All the mass of box are concentrated at the centre of mass i.e., at the centre of gravity.
The box may have the motions of translation and rotation.

Hence , when the force F is applied, the box tends to rotate about the centre of gravity and the box will not tend to rotate about any other point except at the centre of gravity.

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