Question

If area (A), velocity (v), and density ($\rho$) are base units, then the dimensional formula of force can be represented as :-

• A. Av$\rho$
• B. A$v^2\rho$
• C. A$v\rho^2$
• D. $A^2v\rho$

Answer 1

Answer: (B)

A$v^2\rho$

Answer 2

Using the same approach as in the similar question, the force generated by the water stream (by the rate of change of momentum) is given by:

$$F = \frac{d}{dt}(\text{momentum}) = \frac{d}{dt}(mv)$$

where the mass $m$ of the water is given by

$$m = \rho A l \quad \text{(with $l$ being the length traversed)}$$

Since $\frac{dl}{dt} = v$, we get

$$F = \rho A v \times v = \rho A v^2$$

Thus, the dimensional formula for force, when area $(A)$, velocity $(v)$ and density $(\rho)$ are taken as the base units, is represented as:

$$A v^2 \rho$$