Question

A mass M is divided into two parts xm and (1-x)m.The gravitational attraction between the two pieces becomes maximum is ​

Answer 1

Answer:

I hope this is the correct answer ☺️

Answer 2

A mass M is divided into two parts xM and (1 - x)M. let both are seperated in r distance.

using gravitational force, F = Gm1m2/r²

or, F = GxM × (1 - x)M/r²

or, F = GM²/r² (x - x²)

for getting maximum force, differentiate F with respect to x,

dF/dx = GM²/r² (1 - 2x)

now, find value of x at dF/dx = 0

i.e., GM²/r² (1 - 2x) = 0

⇒x = 1/2

now, again differentiate , d²F/dx² = -GM²/r² < 0 hence, at x = 1/2 F will be maximum.

so, F = GM²/r² (1/2 - 1/2²)

= GM²/r² (1/2 - 1/4)

= GM²/4r²