Question

Two bodies of masses $m_1=5\text{kg}$ and $m_2=10\text{kg}$ are placed on $x-$axis $2\text{m}$ apart. If origin has to be taken at mass $m_1$, the gravitational force on $m_2$ is represented as:

Answer 1

Given:
$m_1=5\text{kg};m_2=10\text{kg}$


${\overrightarrow{F}}_{21}=\frac{G{m}_1{m}_2}{r^2}\hat{r}$

Here $\hat{r}$ is along the position vector $\left(\overrightarrow{r}\right)$ of mass $m_1$ w.r.t $m_2$

$\Rightarrow {\overrightarrow{F}}_{21}=\frac{G{m}_1,m_2}{r^3}\overrightarrow{r}$

$(\because \overrightarrow{r}=(0-2)\hat{i}=-2\hat{i})$

$\Rightarrow {\overrightarrow{F}}_{21}=\frac{G\left(5\right)\left(10\right)}{(2{)}^3}(-2\hat{i})$

$\Rightarrow {\overrightarrow{F}}_{21}=-[\frac{50}{8}\times 2]G\hat{i}$

$\therefore {\overrightarrow{F}}_{21}=-\frac{25G}{2}\hat{i}$

Hence, option $\left(b\right)$ is correct.

$$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: While using Newton's law of}\\ \text{gravitation in vector forms, the}\overrightarrow{r}\\ \text{represent position vector of one mass}\\ \text{w.r.t other keeping in mind the}\\ \text{direction of force on body.}\end{array}$$