I read this phrase in a book..."If the gravitational force has to be maximum,then dF/dm has to be zero"

Question

How?...and why?

Answer 1

I am not sure what the context is, but if m is mass, I am presuming they are calculating how the force varies with changing mass; the notation dF/dm means how much change in force will occur if the mass changes by a small amount.

If you have taken calculus, then you are familiar that the first derivative of a function is zero whenever the function is a max or min; this occurs because when a function is at its highest (or lowest) point, it is neither increasing nor decreasing at that moment, and so, mathematically, we know that its derivative---its rate of change---is zero at that moment.

That is why the book says "If...maximum, dF/dm=0"

hope this helps

Answer 2

Gravitational force is inversely proportional to mass. Hence dF/dm cannot be zero if F refers to the force and m refers to the mass.

dF/dm = K /(m*m) where K is a constant

dF/dm can only be zero for m = infinity. This can only happen at speeds equal to the speed of light which is unachievable.

Answer 3

F = mg so dF/dm = g.

I think you mean dF/dx = 0. Which means that gravity does not change with distance, which happens at a maximum OR a minimum, or a point of inflection for that matter.

Answer 4

Hey, Spooky, this is your homework huh!, I hope the other guy helped you. Peace!