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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
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B
35
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C
1
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D
2
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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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