Question

Check the validity of the equation: PV = mv^{​​​​​2}​​​​- mgh.Symbols have usual meanings

Answer 1

if p=momentum which is mass*velocity
then this equation is dimensionaly valid.It does not mean that this equation is true.we cannot determine whether an equation is correct unless we dont know the context.But the dimensional correctness of the equation can be determined.

PV = mv^{​​​​​2}​​​​- mgh
p=momentum=mass*velocity
dimension of mass M
dim of velocity=LT^-1
dimension of LHS=M(LT^-1)^2=M(L^2)(T^-2)
coming to RHS
dim of mv^2=M(L^2(T^-2)
we have to check the dim of mgh
dim of m=M
dim of g=dim of acceleration=LT^-2
dim of h=L
dim of mgh=M(L^2)(T^-2)
so dim of all the terms in the equation is same hence the equation is dimensionaly correct
PS :THIS DOES NOT MEAN THAT THE EQN IS CORRECT .IT MAY OR MAY NOT BE CORRECT BUT IT IS DIMENSIONALY VALID.WHEN AN EQUATION IS DIMENSIONALY INVALID IT WILL SURELY BE WRONG AT ANY CIRCUMSTANCES