Question

Check whether the equation mv² = mgh
is dimensionally consistent Based
on the above equation justify the
following statement
A dimensionally correct equation
need not be actually an exact
equation"​

Answer 1

Explanation:

Dimension of m = [ M ]

Dimension of v = [ L T^(-1) ]

Dimension of g = [ L T^(-2) ]

Dimension of h = [ L ]

Therefore, dimension of LHS:

= > [ M ] [ L T^(-1) ]^2

= > [ M ] [ L^(2) T^(-2) ]

= > [ M L^(2) T^(-2) ]

dimension of RHS:

= > [ M ] [ L T^(-2) ] [ L ]

= > [ M L T^(-2) L ]

= > [ M L^(2) T^(-2) ]

Dimensions of LHS = dimensions of RHS

Hence this equation is dimensionally correct.

Since both the equation represent different things, mv^2 represent 2* kinetic energy while mgh represents potential energy. Hence we can say

A dimensionally correct equation need not be actually an exact