Question

Check the accuracy of E=mgh+1/2mv2

Answer 1

If you mean dimension wise,
As we know Energy=Joules/Second or M¹L²T`²
This will be RHS, now we if if it is dimensionally correct we would have to prove R.H.S=L.H.S

For L.H.S
mass=M
g= acceleration =L¹T`²
v= dist/time= L¹T`¹

Adding as per question

[M][LT`²][L] + (ignore 1/2 cause its constant) [M][LT`1]

==> [M²L³T`³]

since R.H.S ≠L.H.S

*its not accurate*

(`) is used instead of (-) Sorry.

Answer 2

Explanation:

E =ML2T-2 (energy)

m =M. (mass)

g=LT-2. (acceleration due to gravity)

h=L. (height)

I= ML2. ( momentum of inertia)

W=T-1. (angular velocity)

[ML2T-2] = [MxLT-2xL]+ [ML2xT-2]

[ML2T-2]= [ML2T-2]. (only same dimensions can be added and subtract)

LHS=RHS