Question

Three identical point masses, each of mass $1 \,kg$ lie in the $x - y$ plane at points $(0, 0), (0, 0.2m)$ and $(0.2m, 0)$. The net gravitational force on the mass at the origin is

• A. $1.67 \times 10^{-9} (\hat{i} + \hat{j})N$
• B. $3.34 \times 10^{-10} (\hat{i}+ \hat{j})N$
• C. $1.67 \times 10^{-9} (\hat{i} - \hat{j})N$
• D. $3.3 4 \times 10^{-10}(\hat{i} + \hat{j}) N$

Answer 1

Answer: (A)

Let particle $A$ lies at origin, particle $B$ and $C$ on $y$ and $x$ -axis respectively

$\vec{F}_{AC} = \frac{Gm_Am_B}{r^2_{AB}} \hat{i}$
$ = \frac{6.67 \times 10^{-11} \times 1 \times1}{(0.2)^2} \hat{i}$
$ = 1.67 \times 10^{-9} \hat{i} N$
Similarly $\vec{F}_{AB} = 1.67 \times 10^{-9} \hat{j} N$
$\therefore $ Net force on particle $A$
$\vec{F} = \vec{F}_{AC} + \vec{F}_{AB} $
$= 1.67 \times 10^{-9} ( \hat{i} + \hat{j}) N$