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Discuss the vector form of gravitational force between two masses with the help of diagram.

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1. Consider two point masses m and m having position vectors \(\overrightarrow{r}_1\) and \(\overrightarrow{r}_2\) from origin O respectively as shown in figure.

2. The position vector of mass m with respect to m1 is given by,

3. Similarly, position vector of mass m with respect to m2 is,

4. Let \(|\overrightarrow{r_{12}}|=|\overrightarrow{r_{21}}|\) Then, the force acting on mass m2 due to mass m1 will be given as,

where, \(\hat{r}_{21}\) is the unit vector from m1 to m2.

The force \(\overrightarrow{F_{21}}\) is directed from m2 to m1.

5. Similarly, force experienced by m1 due to m2 is given as,

[Note: As \(\hat{r}_{21}\) is defined as unit vector from m1 to m2, conceptually force \(\overrightarrow{F}_{21}\) is directed from m2 lo m1.]

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