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
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
$0.5$
$\frac{3}{5}$
$1$
$2$
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
$F \propto xm \times (1 - x)m = x{m^2}(1 - x)$
For maximum force $\frac{{dF}}{{dx}} = 0$
$⇒$ $\frac{{dF}}{{dx}} = {m^2} - 2x{m^2} = 0\, \Rightarrow x = 1/2$
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