To determine the correct SI unit for momentum, let's step through the concept and principles involved:
1. Understanding Momentum:
- Momentum is a measure of the quantity of motion an object has.
- The formula for momentum ([tex]\( p \)[/tex]) is given by:
[tex]\[
p = m \cdot v
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object.
- [tex]\( v \)[/tex] is the velocity of the object.
2. SI Units for Mass and Velocity:
- The SI unit for mass ([tex]\( m \)[/tex]) is kilograms ([tex]\( kg \)[/tex]).
- The SI unit for velocity ([tex]\( v \)[/tex]) is meters per second ([tex]\( \frac{m}{s} \)[/tex]).
3. Combining Units:
- When we multiply the mass ([tex]\( kg \)[/tex]) by the velocity ([tex]\( \frac{m}{s} \)[/tex]), we get:
[tex]\[
p = kg \times \frac{m}{s}
\][/tex]
4. Checking Given Options:
- The first option, ([tex]\( kg \cdot m \)[/tex]), is not correct because it does not consider the velocity component of momentum.
- The second option, ([tex]\( kg \cdot \frac{m}{s} \)[/tex]), correctly combines the units of mass and velocity.
- The third option, ([tex]\( kg = \frac{m^2}{s} \)[/tex]), is incorrect as it doesn't match the dimensions required for momentum.
- The fourth option, ([tex]\( kg \cdot \frac{m}{s^2} \)[/tex]), is incorrect as it represents the unit for force (Newton), not momentum.
Thus, the SI unit for momentum is [tex]\(\boxed{kg \cdot \frac{m}{s}}\)[/tex]. Among the given options, this corresponds to the second choice.
