Check the dimensional consistency of the following equations.
(i) de brogile's wavelength ,λ=h/mv
(ii)Escape velocity,v=√2GM/R
Please refer to the given below link to get the dimensions of de-broglie wavelength:-
https://www.meritnation.com/ask-answer/question/what-is-the-dimension-of-de-broglie-wavelength-plz-tell/physics/5410438
As, escape velocity is given by:-
v= ..........(1) where G is the gravitational constant, M and R are respectively mass and radius of the
earth.
As, dimensions of G= M-1L3T-2
dimensions of M and R are respectively M and L.
Substitute dimensions of G, M and R in eq. (1):-
We get:-
Dimension of escape velocity= LT-1 which is same as the dimension of velocity of the body.
https://www.meritnation.com/ask-answer/question/what-is-the-dimension-of-de-broglie-wavelength-plz-tell/physics/5410438
As, escape velocity is given by:-
v= ..........(1) where G is the gravitational constant, M and R are respectively mass and radius of the
earth.
As, dimensions of G= M-1L3T-2
dimensions of M and R are respectively M and L.
Substitute dimensions of G, M and R in eq. (1):-
We get:-
Dimension of escape velocity= LT-1 which is same as the dimension of velocity of the body.