Question

A physical quantity has term of velocity,and force which are proportional to it .It is known that it does not depend on any other physical quantity ,so its dimension can be,

• A. $M{L}^2{T}^{-3}$
• B. $ML{T}^3$
• C. $M{L}^2{T}^3$
• D. none of the above

Answer 1

The correct option is A $M{L}^2{T}^{-3}$

Let, $x$ be the physical quantity.

Here, $x\propto v$ a$x\propto F$ where $v=$ velocity and $F=$ force

$x=kvF$ where $k=$ proportionality constant.

Dimensionally, $\left[x\right]=\left[L{T}^{-1}\right]\left[ML{T}^{-2}\right]=\left[M{L}^2{T}^{-3}\right]$