Two point objects of mass 2x and 3x are separ | vedclass

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(C) Let $y$ be the amount of mass transferred from the object with mass $3x$ to the object with mass $2x$.After the transfer,the new masses are $(3x -

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$\frac{x}{2}$

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(C) Let $y$ be the amount of mass transferred from the object with mass $3x$ to the object with mass $2x$.After the transfer,the new masses are $(3x - y)$ and $(2x + y)$.The gravitational force between them is given by $F' = \frac{G(3x - y)(2x + y)}{r^2}$.To maximize the force,we differentiate $F'$ with respect to $y$ and set it to zero:$\frac{dF'}{dy} = \frac{G}{r^2} \frac{d}{dy} [6x^2 + 3xy - 2xy - y^2] = 0$.$\frac{G}{r^2} [3x - 2x - 2y] = 0$.$x - 2y = 0$.$y = \frac{x}{2}$.Thus,the mass to be transferred is $\frac{x}{2}$.

Two point objects of mass $2x$ and $3x$ are separated by a distance $r$. Keeping the distance fixed,how much mass should be transferred from $3x$ to $2x$,so that the gravitational force between them becomes maximum?

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