Question

X=PV+Q/P+T, find the dimensions of P and Q .(where x=distance,v= velocity, t= time)??​

Answer 1

$\boxed{x = Pv + \dfrac{Qt}{P}}$

Now, we know that only quantities with similar dimensions can be added :

$[Pv] = [x]$

$\implies [P \times L{T}^{ - 1} ] = [L]$

$\implies [P ] = [T]$

So, dimension of P is [T].

$[\dfrac{Qt}{P}] = [x]$

$\implies [\dfrac{Q \times T}{T}] = [L]$

$\implies [Q] = [L]$

So, Dimension of Q is [L].

Answer 2

Answer:

$\boxed{x = Pv + \dfrac{Qt}{P}}x=Pv+PQt</p><p></p><p>Now, we know that only quantities with similar dimensions can be added :</p><p></p><p>[Pv] = [x][Pv]=[x]</p><p></p><p>\implies [P \times L{T}^{ - 1} ] = [L]⟹[P×LT−1]=[L]</p><p></p><p>\implies [P ] = [T]⟹[P]=[T]</p><p></p><p>So, dimension of P is [T].</p><p></p><p>[\dfrac{Qt}{P}] = [x][PQt]=[x]</p><p></p><p>\implies [\dfrac{Q \times T}{T}] = [L]⟹[TQ×T]=[L]</p><p></p><p>\implies [Q] = [L]⟹[Q]=[L]</p><p></p><p>So, Dimension of Q is [L].</p><p></p><p>$

solution by rohit.