gravitaional intensity(E)=F/m and acc=F/m... mathatically and dimensionally E=acc. but scientifically E is not equal to acc.

Gravitational Intensity(E) of a body at a point in the field is defined as the force experienced by a body of unit mass placed at that point provided the presence of unit mass does not disturb the original gravitational field.Thus,
E = F/m
If m=1kg then,
E = F
Now acceleration of an body is gven as,\
a = F/m
but a = F when m =1Kg
thus on this basis gravitational intensity(E) will be equal to the acceleration of the body(a).But actually the gravitational intensity at a point distance ‘r ‘from the centre of the body of mass ‘M’ is given as,
E = GM/r2 which is acceleration due to gravity i.e g.So E = g acceleration due to gravity and not ‘a‘ which is acceleration of an body.

The force related to a = F/m is the Newtonian Force (Related to momentum of the body). But the force related to Gravitational field intensity (E = F/m) is the force of attraction between two bodies is just like the force between two charge bodies in electrostatic (Coulomb Force). Therefore the Newtonian force is not equal to Gravitational force even if dimensionally. That is why; scientifically gravitational field intensity (E) is not equal to acceleration of the body (a).

Dear student,
The Gravitational Intensity is represented by Acceleration due to gravity and it is directed towards the surface of earth. Whereas in general the acceleration is directed along other directions depending on the direction of the applied force.
So, please dont get confused whether scientifically they are not equal.
Regards
Sumit