How much momentum will a dumbbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s^{−2}.

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#### Solution

Mass of the dumbbell, *m* = 10 kg

Distance covered by the dumbbell, *s* = 80 cm = 0.8 m

Acceleration in the downward direction, *a* = 10 m/s^{2}

Initial velocity of the dumbbell, *u* = 0

Final velocity of the dumbbell (when it was about to hit the floor) = *v*

According to the third equation of motion:

*v*^{2} = *u*^{2} + 2*as*

*v*^{2} = 0 + 2 (10) 0.8

*v* = 4 m/s

Hence, the momentum with which the dumbbell hits the floor is

= *mv* = 10 × 4 = 40 kg m s^{−1}

Concept: Newton's Second Law of Motion

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