Question

The dimensions of $\frac{\alpha }{\beta }$ in the equation $F=\frac{\alpha -t^2}{\beta v^2}$, where F is the force, v is velocity and t is time, is

• A. $\left[ML{T}^{-1}\right]$
• B. $\left[M{L}^{-1}{T}^{-2}\right]$
• C. $\left[M{L}^3{T}^{-4}\right]$
• D. $\left[M{L}^2{T}^{-4}\right]$

Answer 1

The correct option is C $\left[M{L}^3{T}^{-4}\right]$

$F{V}^2$ = $\frac{\alpha }{\beta }$ -$\frac{t^2}{\beta }$

or $\frac{\alpha }{\beta }$ has dim. of $F{V}^2$

= $ML{T}^{-2}{L}^2{T}^{-2}$ = $M{L}^3{T}^{-4}$

Hence C is correct