How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm ? Take its downward acceleration to be `10 ms ^(-2)`.

Explanation

Mass, m = 10 kg
Height or Distance , s = 80 cm
`= (80)/(100) = 0.8 m`
Acceleration, `a = 10 ms^(-2)`
Initial velocity , `u = 0 ms^(-1)`
By third equation of motion,
`v^(2) - u^(2) = 2a s`
`rArr v^(2) - (0 ms^(-1))^(2)`
`= 2 xx 10ms^(-2) xx 0.8 m`
`rArr v^(2) = 16 ms^(-1)`
`rArr v = 4 ms^(-1)`
Momentum transferred to the floor
`= m xx v`
`= 10 kg xx 4 ms^(-1)`
`= 40 kg ms^(-1)`