Question

What is the dimensional formula of momentum?
${\text{A}}{\text{.}}$ MLT
\[
  {\text{B}}{\text{. }}{{\text{M}}^{ - 1}}{{\text{L}}^{ - 1}}{{\text{T}}^{ - 1}} \\
  {\text{C}}{\text{. M}}{{\text{L}}^{ - 1}}{{\text{T}}^{ - 1}} \\
  {\text{D}}{\text{. ML}}{{\text{T}}^{ - 1}} \\
 \]

Answer 1

Hint: Here, we will proceed by finding the dimensional formula of velocity in terms of primary dimensions. Then, we will be substituting this dimensional formula in the formula used to determine momentum.
Formulas Used: Velocity = $\dfrac{{{\text{Displacement}}}}{{{\text{Time}}}}$ and Momentum = (mass)(velocity).

Complete Step-by-Step solution:
As we know that the dimension of mass m is given by
Dimension of mass m = [M]
Also, we know that the formula to determine velocity is as under
Velocity = $\dfrac{{{\text{Displacement}}}}{{{\text{Time}}}}{\text{ }} \to {\text{(1)}}$
Since, displacement is simply length so the dimension of displacement will be equal to [L]
The dimension of time is given by
Dimension of time = [T]
By applying dimensional analysis on the formula given by equation (1), we get
Dimension of velocity = $\dfrac{{{\text{Dimension of displacement}}}}{{{\text{Dimension of time}}}} = \dfrac{{\left[ {\text{L}} \right]}}{{\left[ {\text{T}} \right]}} = \left[ {\text{L}} \right]\left[ {{{\text{T}}^{ - 1}}} \right] = \left[ {{\text{L}}{{\text{T}}^{ - 1}}} \right]$
So, the dimension of velocity is $\left[ {{\text{L}}{{\text{T}}^{ - 1}}} \right]$
Also, the momentum of any body is equal to the product of its mass and velocity
i.e., Momentum = (mass)(velocity)
By applying dimensional analysis on the above formula, we get
Dimension of momentum = (Dimension of mass)(Dimension of velocity) = [M]$\left[ {{\text{L}}{{\text{T}}^{ - 1}}} \right]$ = $\left[ {{\text{ML}}{{\text{T}}^{ - 1}}} \right]$
Therefore, the dimensional formula of momentum is $\left[ {{\text{ML}}{{\text{T}}^{ - 1}}} \right]$.
Hence, option D is correct.

Note- There are seven primary dimensions in units of measurement. The primary dimensions are defined as independent or fundamental dimensions from which other dimensions can be derived. The primary dimensions are mass, length, time , temperature, electric current, quantity of light and quantity of matter.