Two particles of mass m and 9m are separated | vedclass

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Question

(C) For the gravitational field to be zero,the intensities produced by both particles must be equal in magnitude and opposite in direction.$\frac{G m}

Vedclass · Accepted Answer

$-\frac{16 G m}{r}$

Vedclass · Answer

(C) For the gravitational field to be zero,the intensities produced by both particles must be equal in magnitude and opposite in direction.$\frac{G m}{r_1^2} = \frac{G(9 m)}{r_2^2}$where $r_1$ is the distance from mass $m$ and $r_2$ is the distance from mass $9m$.Since $r_1 + r_2 = r$,we have $\frac{r_2}{r_1} = \sqrt{9} = 3 \Rightarrow r_2 = 3 r_1$.Therefore,$r_1 + 3 r_1 = r \Rightarrow 4 r_1 = r \Rightarrow r_1 = \frac{r}{4}$ and $r_2 = \frac{3r}{4}$.The gravitational potential $V$ is given by $V = -\frac{G m}{r_1} - \frac{G(9 m)}{r_2}$.Substituting the values: $V = -\frac{G m}{r/4} - \frac{9 G m}{3r/4} = -\frac{4 G m}{r} - \frac{36 G m}{3r} = -\frac{4 G m}{r} - \frac{12 G m}{r} = -\frac{16 G m}{r}$.

Two particles of mass $m$ and $9m$ are separated by a distance $r$. At a point on the line joining them,the gravitational field is zero. What is the gravitational potential at that point? ($G$ is the universal gravitational constant)

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