Question

An athlete’s coach told him that muscle times speed equals power. Then according to him the dimensions of muscles are
A- $[ML{{T}^{-2}}]$
B- $[M{{L}^{2}}{{T}^{-2}}]$
C- $[ML{{T}^{2}}]$
D- $[ML{{T}^{-3}}]$

Answer 1

This is a problem of dimensional analysis. We can deduce the value from the dimensional formula of these individual elements by finding the degree of dependence of a physical quantity on another. The principle of consistency of two expressions can be used to find the equation relating these two quantities.

Complete step by step answer: An athlete’s coach told him that muscle times speed equals power, writing this as an equation,
Power= muscle $\times$speed
So, muscle= $\dfrac{P}{v}$
Dimensional formula for velocity/speed is $[L{{T}^{-1}}]$ and for the power it is $[M{{L}^{2}}{{T}^{-3}}]$ so, putting in the above equation we get muscle= $\dfrac{[M{{L}^{2}}{{T}^{-3}}]}{[L{{T}^{-1}}]}=[ML{{T}^{-2}}]$
So, this matches with the given option (A), hence the correct option is (A).

Additional information: Dimensional analysis is also called Factor Label Method. Using the dimensional analysis, we can check the correctness of Physical Equation. However, it should be kept in mind that dimensional analysis cannot help us determine any dimensionless constants in the equation. This method also used chemistry and there in place of using designated symbols we use units.

Note:
Though this method is widely used, there are few drawbacks for this method. Dimensionless quantities cannot be determined by this method. Constant proportionality cannot be determined by this method. It does not apply to trigonometric, logarithmic and exponential functions physical quantities which are dependent upon more than three physical quantities, this method will be difficult.