Question

How much momentum will a dumbbell of mass $10kg$ transfer to the floor if it falls from a height of $80cm$ (assume that the dumbbell stops after hitting the ground, g=$10m{s}^{-2}$)?

• A. 40 kg m/s
• B. 50 kg m/s
• C. 30 kg m/s
• D. 35 kg m/s

Answer 1

The correct option is A

40 kg m/s

Mass of the dumbbell $m$= 10 kg

Distance covered by the dumbbell $S=80cm=0.8m$

Acceleration in the downward direction $a=10m{s}^{-2}$

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:
$v^2-u^2=2as\Rightarrow v=\sqrt{u^2+(2\times a\times s)}$
$\Rightarrow v=\sqrt{0+(2\times 10\times 0.8)}$
$=4m{s}^{-1}$
Hence, the momentum with which the dumbbell hits the floor is:
$m\times v=10\times 4=40kgm{s}^{-1}$.