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The smaller object will have a larger acceleration than the larger object.

This is because, from Newton's second law, the acceleration of a body is given by:

a = F/m

where

a is acceleration

F is resultant force

and m is mass

F is constant, so acceleration is inversely proportional to mass.

Hence, the smaller object will have a larger acceleration.

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Q: Does a smaller object with the same force will accelerate the same than a larger object?
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