Question

A ball has m=10 kg and v=10 m/s. It has the same momentum as which of the following?

Select one:
a. A ball with m = 100 kg and v = 1 m/s.
b. A ball with m = 5 kg and v = 20 m/s.
c. A ball with m = 2 kg and v = 50 m/s
d. all of these

Answer 1

Choice d. All three balls listed in choice a, b, and c have a momentum of
`100\; \rm kg \cdot m \cdot s^(-1)` each, same as that of the
`10\; \rm kg` ball moving at
`10\; \rm m \cdot s^(-1)`. Assumption: all four balls are moving in the same direction.

Step-by-step explanation:

The momentum
`p` of an object is equal to the product of its mass
`m` and its velocity
`v`.

Momentum of a
`10\; \rm kg` ball moving at
`10\; \rm m \cdot s^(-1)`:

`p = m \cdot v = 10\; \rm kg * 10\; \rm m \cdot s^(-1) = 100\; \rm kg \cdot m \cdot s^(-1)`.

Similarly:

• Momentum of the ball in choice a:
  `100 \; \rm kg * 1\; \rm m \cdot s^(-1) = 100\; \rm kg \cdot m\cdot s^(-1)`.
• Momentum of the ball in choice b:
  `5 \; \rm kg * 20\; \rm m \cdot s^(-1) = 100\; \rm kg \cdot m\cdot s^(-1)`.
• Momentum of the ball in choice c:
  `2 \; \rm kg * 50\; \rm m \cdot s^(-1) = 100\; \rm kg \cdot m\cdot s^(-1)`.

Hence the conclusion that these balls have the same momentum.