A quick conception question Newtonian physics

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quantumtron
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i was having an argument with my friend.

He claims that acceleration for object that is lighter, let say a stone (1000kg) and ball (1kg). If we were to throw them up in the sky with the same initial speed, their acceleration would always be 9.81ms^2 (depending on sign conventions). Am i right to say that?

My friend claims that the acceleration for the lighter object would be greater...
 
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