Question

# Mass $$m$$ is divided into two parts $$X\ m$$ and $$(1-X)\ m$$. For a given separation, the value of $$X$$ for which the gravitational force of attraction between the two pieces becomes maximum is :

A
12
B
35
C
1
D
2

Solution

## The correct option is A $$\dfrac{1}{2}$$Force  exerted  by  the  bodies  is  given  by  $$F = \dfrac{GmmX(1-X)}{R^2}$$For maximum force ,  $$X(1-X)$$ should be maximum.Differentiating  $$X(1-X)$$ gives  $$1-2*X=0$$  or  $$X =\dfrac{1}{2}$$Physics

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