You lay a pencil on a smooth desk ignore sliding friction Yo

You lay a pencil on a smooth desk (ignore sliding friction). You push the pencil, exerting a constant force first directly at its center of mass and then close to the tip of the pencil. In both cases, the force that you exert on the pencil are exactly the same in magnitude and direction, in which case is the translational acceleration of the pencil greater in magnitude?

Solution

If force is applied at the center of mass of the pencil, it moves is straight path without rotating as the center mass is the position where the wieght of the pencil is balanced. When the force is applied at the tip of the pencil it moves in more in rotational motion rather than translational motion. Therefore, the pencil will have more translational acceleration when the force is applied at its centre of mass.