Question

What is the SI unit of momentum?
\[\begin{align}
  & \text{a}\text{. }dyne.sec \\
 & \text{b}\text{. gcm}{{\text{s}}^{-1}} \\
 & \text{c}\text{. }N.s \\
 & \text{d}\text{. }gm.s \\
\end{align}\]

Answer 1

Hint: Convert the mathematical formula of momentum into basic units of SI system and try matching it with options. For example, force is defined as the change in momentum with respect to time.

Complete step by step answer:
The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.

Second (the unit of time with the symbol s),
Meter (length, m),
Kilogram (mass, kg),
Ampere (electric current, A),
Kelvin (thermodynamic temperature, K),
Mole (amount of substance, mol)
Candela (luminous intensity, cd).

Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. It is a vector quantity, which means it has both a magnitude and a direction. It is represented by p.

$\text{F=}\dfrac{\text{dp}}{\text{dt}}$

Where,

\[\begin{array}{*{35}{l}}
   dp\text{ }=\text{ change in momentum} \\
   dt\text{ }=\text{ time} \\
\end{array}\]

So, we can write as

\[dp=\text{ }F.dt\]

SI unit of force is N
SI unit of time is s
SI unit of momentum is N.s

So correct option (c)

Additional Information:
Momentum is the product of the mass and velocity of an object. If m is an object's mass and v is its velocity then the object's momentum is

P=mv
SI unit of mass (m) is Kg
SI unit of velocity is $\dfrac{\text{m}}{\text{s}}$
So, the unit of momentum is $\dfrac{\text{Kg m}}{\text{s}}$

Momentum can be thought of as the "power" when a body is moving, meaning how much force it can have on another body. For example, a bowling ball (large mass) moving very slowly (low velocity) can have the same momentum as a baseball (small mass) that is thrown fast (high velocity).

Note: Firstly, students should convert the given formula into the known formulas and then write the units to get dimensional formula or SI units. Secondly, other options are in terms of MKS units. For example, option a) Dyne is the unit of force in the MKS system, similarly, in option b) and d) centimetres and grams are in MKS units. Therefore, the correct option for the SI unit is only c).