Question

How much momentum does a dumbbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm, assuming 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

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