Sure! Let's analyze the given options to determine which units are similar.
1. [tex]\( N - S \)[/tex]:
- This represents Newton-Second (N·s), which is a unit of impulse or momentum. An impulse is the force applied over a period of time, and when a force [tex]\( F \)[/tex] is applied over a time [tex]\( t \)[/tex], the resulting impulse is [tex]\( F \cdot t \)[/tex]. Momentum is mass [tex]\( \times \)[/tex] velocity, which has the same dimensional units as impulse.
2. [tex]\( N \)[/tex]:
- This represents Newton (N), which is a unit of force. One Newton is the force needed to accelerate a one-kilogram mass by one meter per second squared (1 N = 1 kg·m/s²).
3. [tex]\( \frac{kg \cdot m}{s} \)[/tex]:
- This represents Kilogram meter per second (kg·m/s), which is a unit of momentum. When we consider the mass (kg) times its velocity (m/s), we get the momentum.
4. "both 183":
- This is not a standard unit of measurement and does not correspond to any known physical quantity.
Now, let’s compare these units:
- [tex]\( N - S \)[/tex] (Newton-Second) and [tex]\( \frac{kg \cdot m}{s} \)[/tex] (Kilogram meter per second) are indeed units of momentum.
- [tex]\( N \)[/tex] (Newton) is a unit of force and does not belong to the same category as the units of momentum.
- "both 183" is not an actual unit, so it can't be compared to the others.
Therefore, the similar units are:
- Option 1: [tex]\( N - S \)[/tex] (Newton-Second)
- Option 3: [tex]\( \frac{kg \cdot m}{s} \)[/tex] (Kilogram meter per second)
The correct answer is (1, 3).
