Gravitation Question 288

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 attraction between the two pieces becomes maximum is [EAMCET 2001]

Options:

A)$ [\frac{1}{2}] $

B)$ [\frac{3}{5}] $

C) 1

D) 2

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Answer:

Correct Answer: A

Solution:

$ [F\propto xm\times (1-x)m=xm^{2}(1-x)] $

For maximum force $ [\frac{dF}{dx}=0] $

Þ$ [\frac{dF}{dx}=m^{2}-2xm^{2}=0\Rightarrow x=1/2] $



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