Answer:
Choice d. All three balls listed in choice a, b, and c have a momentum of [tex]100\; \rm kg \cdot m \cdot s^{-1}[/tex] each, same as that of the [tex]10\; \rm kg[/tex] ball moving at [tex]10\; \rm m \cdot s^{-1}[/tex]. Assumption: all four balls are moving in the same direction.
Explanation:
The momentum [tex]p[/tex] of an object is equal to the product of its mass [tex]m[/tex] and its velocity [tex]v[/tex].
Momentum of a [tex]10\; \rm kg[/tex] ball moving at [tex]10\; \rm m \cdot s^{-1}[/tex]:
[tex]p = m \cdot v = 10\; \rm kg \times 10\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m \cdot s^{-1}[/tex].
Similarly:
- Momentum of the ball in choice a: [tex]100 \; \rm kg \times 1\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].
- Momentum of the ball in choice b: [tex]5 \; \rm kg \times 20\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].
- Momentum of the ball in choice c: [tex]2 \; \rm kg \times 50\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].
Hence the conclusion that these balls have the same momentum.
