Question

Write formula and derive dimensions of force​

Answer 1

Answer:

The dimensional formula of force is mentioned below:

• ${\small{\underline{\boxed{\pmb{\sf{M^1L^1T^{-2}}}}}}}$

Now let us derive the dimensional formula of force:

By using dimensional analysis!

$\begin{gathered}:\implies \sf Force \: = Mass \times Acceleration \\ \\ :\implies \sf Force \: = [M^1] \times \dfrac{\Delta v}{t} \\ \\ :\implies \sf Force \: = [M^1] \times \dfrac{Displacement}{Time \times Time} \\ \\ :\implies \sf Force \: = [M^1] \times \dfrac{[L]}{[T^2]} \\ \\ :\implies \sf Force \: = [M^1L^1T^{-2}]\end{gathered}$

• Henceforth, the dimension formula of force is ${\sf{[M^1L^1T^{-2}]}}$