Question

Given that "mass" multiply by constant “k” is equal to "energy" divided by “height”. Determine, by using dimensions of each, which physical quantity is represented by “k”?

Answer 1

Given:

"mass" multiply by constant “k” is equal to "energy" divided by “height”.

To find:

Which physical quantity is represented by "k" ?

Calculation:

We will use dimensional analysis to solve this kind of questions :

$\therefore \: \bigg \{mass \times k \bigg \} = \bigg \{ \dfrac{energy}{height} \bigg \}$

Expressing all the physical quantities in terms of Mass, Length and Time :

$\implies \bigg \{ M\times k \bigg \} = \bigg \{ \dfrac{M{L}^{2} {T}^{ - 2} }{L} \bigg \}$

$\implies \bigg \{ k \bigg \} = \bigg \{ \dfrac{{L}^{2} {T}^{ - 2} }{L} \bigg \}$

$\implies \bigg \{ k \bigg \} = \bigg \{ L {T}^{ - 2} \bigg \}$

$\implies \bigg \{ k \bigg \} = \bigg \{ acceleration\bigg \}$

So, "k" represents "acceleration".

$\boxed{ \bold{ \bigg \{ k \bigg \} = \bigg \{ acceleration\bigg \}}}$