**Dimensional Analysis**

Dimensional analysis is a powerful tool used in physics to analyze and derive relationships between physical quantities. It involves studying the dimensions or units of different physical quantities and using them to determine the dimensions of other quantities.

**Fundamental Units**

In this question, three fundamental units are given: frequency (F), velocity (V), and density (D). These units are considered fundamental because they cannot be expressed in terms of other physical quantities.

**Momentum**

Momentum is defined as the product of mass and velocity. It is a fundamental concept in physics and is given by the formula:

Momentum = mass × velocity

In dimensional analysis, we express physical quantities in terms of their fundamental units. So, to determine the dimensional formula for momentum, we need to express mass and velocity in terms of the given fundamental units.

**Mass**

Mass is a fundamental quantity and can be expressed in terms of density using the formula:

Mass = density × volume

Since density (D) is already a given fundamental unit, we can express mass in terms of D.

**Velocity**

Velocity is a fundamental quantity and can be expressed in terms of frequency using the formula:

Velocity = frequency × wavelength

Since frequency (F) is already a given fundamental unit, we can express velocity in terms of F.

**Dimensional Formula for Momentum**

Now, let's express momentum in terms of the given fundamental units:

Momentum = mass × velocity

Substituting the expressions for mass and velocity:

Momentum = (density × volume) × (frequency × wavelength)

Since density is given as a fundamental unit (D), we can replace volume with its dimensional formula, which is length cubed (L^3).

Momentum = (D × L^3) × (F × wavelength)

Now, we need to determine the dimensional formula for wavelength. Wavelength is the distance between two consecutive points in a wave and is given by the formula:

Wavelength = velocity / frequency

Substituting the expression for velocity:

Wavelength = (F × wavelength) / F

The frequency terms cancel out, leaving:

Wavelength = velocity

Therefore, the dimensional formula for wavelength is the same as that of velocity (V).

Substituting the expression for wavelength back into the equation for momentum:

Momentum = (D × L^3) × (F × V)

Simplifying further:

Momentum = D × F × L^3 × V

Thus, the dimensional formula for momentum is DFL^3V.

D V4F-3