Question

How much momentum will a dumbbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm (assume that the dumbbell stops after hitting the ground)? (Take g = 10 ms^-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, $s$ = 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,
$v^2-u^2=2as\Rightarrow v=\sqrt{u^2+(2\times a\times s)}$
$\Rightarrow v=\sqrt{0+(2\times 10\times 0.8)}=4\text{m/s}$
Hence, the momentum with which the dumbbell hits the floor is,
m × v = 10 × 4 = 40 kg m/s