Question

Using dimensional analysis,verify the correctness of v=2gh and v=ut/2+at

Answer 1

Dimensional Analysis :

We compare the dimensions of the quantities on both sides of the equation, and we can say if a equation is wrong or correct. Even though, A equation which may be dimensionally correct may not be a valid equation.

Formula 1 : v=2gh

Velocity $= [LS^{-1}] \:$

g = Acceleration due to gravity = $= [LS^{-2}] \:$

h $= [L] \:$

Now,

$L. H. S =v = [LS^{-1}] \: \:$

$R. H. S= [L] \: \times [LS^{-2}] \\ = [L ^{2} S^{-2}]$

Since, Dimensional equations of LHS and RHS aren't equal, The formula v = 2gh isn't correct.

Formula 2 : v = ut/2 + at

LHS = v $= [LS^{-1}] \:$

RHS = ut/2 + at = $= [LS^{-1}][S] + [LS^{-2}][S] \: \\ = [L] + [LS^{-1}]$

Both, LHS and RHS don't match. Hence, We can conclude that, v = ut/2 + at isn't correct