Question

Mass M is divided into two parts xM and (1 – x) M. For a given separation, the value of x for which the gravitational force between the two pieces becomes maximum is 

(A) 1 

(B) 2 

(C) 1/2 

(D) 4/5

Answer 1

Correct option: (C) 1/2

Explanation:

F = [(Gm₁m₂) / r²]

i.e.  F ∝ m₁m₂ 

F ∝ mx(1 – x)m

F ∝ m² ∙ x(1 – x)

for maximum force

(dF / dx) = 0

(d/dx) = [x(1 – x)m²] = 0

m²[– 2x + 1] = 0

x = (1/2)