Question

Which has the most momentum?

C: Both have the same momentum

B: A 100 g object at 1 m/s

D: Neither has any momentum.

A: A 1 g object at 100 m/s

Answer 1

Both objects have the same magnitude of momentum.

Step-by-step explanation:

If an object of mass
`m` is moving at a velocity of
`v`, the momentum of that object would be
`m\, v`.

The
`100\; {\rm g}` (
`0.1\; {\rm kg}`) object is moving at a speed of
`1\; {\rm m\cdot s^(-1)}`. The magnitude of the momentum of this object would be
`0.1\; {\rm kg} * 1\; {\rm m\cdot s^(-1)} = 0.1\; {\rm kg \cdot m \cdot s^(-1)}`.

Similarly, the momentum of the
`1\; {\rm g}` (
`10^(-3)\; {\rm kg}`) object moving at a speed of
`100\; {\rm m\cdot s^(-1)}` would be
`10^(-3)\; {\rm kg} * 100\; {\rm m\cdot s^(-1)} = 0.1\; {\rm kg \cdot m \cdot s^(-1)}`.

Hence, the magnitude of momentum is the same for the two objects.