What is torque and how does it affect the motion of objects?

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What exactly is torque? Also if a force of 10N was applied to a 10kg block in a location that is not at its center of mass, does the block have a linear acceleration less than 1m/s/s?
 
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Okay so if you have two situations where you push a 10kg block each with the same force, but only one is being pushed at its center of mass, they should require the same force to accelerate. But does one situation require more energy than the other, and is one block harder to push?