Question

we have learnt that Earth's gravitational field strength is 10 N/kg is the same as its acceleration due to free fall (10 m/s/s. even though their units are different, they are said to be dimentionally the same. prove that N/kg is the same as m/s/s

Answer 1

If you have learned it is 10N/kg, you have learned it wrong. Nowhere on Earth is it that value.

Force=mass*acceleration
Newtons=kg*g
g= N/kg, this is the same g you know as 9.8m/s^2