Question

what is the dimensional formula of a/b in w=at²/bv² where w=work,t=time,v=velocity​

Answer 1

Answer:

$\frac{a}{b} = [M^{1}L^{4}T^{-7}]$

Explanation:

Given that,  $w=\frac{at^{2}}{bv^{2}}$    ----------------------(1)

Dimensional formula of work, $w=[M^{1}L^{2}T^{-3}]$

Dimensional formula of time, $t = [T^{1}]$

Dimensional formula of velocity, $v = [L^{1}T^{-1}]$

Now, substituting in (1), we get:

    $[M^{1}L^{2}T^{-3}]=\frac{ a } { b }*\frac{[T^{2}]}{[L^{2}T^{-2}]}$

=> $\frac{a}{b} = [M^{1}L^{4}T^{-7}]$