Q. The gravitational force on $m_{1}$ due to $m_{2}$ is

1499 284 Gravitation Report Error

A

$\frac{G m _{1} m _{2}}{∣ r _{2} - r _{1} ∣ ^{3}} (r_{2} - r_{1})$ $∣ r_{2} - r_{1} ∣$

B

$\frac{G m _{1} m _{2}}{∣ r ˉ _{2} - r ˉ _{1} ∣ ^{2}} (r_{2} - r_{1})$

C

$\frac{G m _{1} m _{2} ( r _{1} - r _{2} )}{∣ r _{1} - r _{2} ∣ ^{3}}$

D

$\frac{G m _{1} m _{2}}{∣ r _{1} - r _{2} ∣ ^{2}} (r_{1} - r_{2})$

Solution:

$m_{2}$ attract $m_{1}$ towards itself.
$F_{12} = \frac{G m _{1} m _{2}}{∣ r ˉ ∣ ^{2}} \overset{r}{^}$ where $r = r_{2} - r_{1}$ and $\overset{r}{^} = \frac{r _{2} - r _{1}}{∣ r _{2} - r _{1} ∣}$
$\Rightarrow F_{12} = \frac{G m _{1} m _{2}}{∣ r _{2} - r _{1} ∣ ^{2}} \cdot \frac{( r _{2} - r _{1} )}{∣ r _{2} - r _{1} ∣}$