Question

Three identical point masses, each of mass $1kg$ 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. $3.34\times 10^{-10}(\hat{i}+\hat{j})N$

Answer 1

Answer: (A)

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



${\vec{F}}_{AC}=\frac{G{m}_A{m}_B}{r_{AB}^2}\hat{i}$

$=\frac{6.67\times 10^{-11}\times 1\times 1}{(0.2{)}^2}\hat{i}$

$=1.67\times 10^{-9}\hat{i}N$

Similarly ${\vec{F}}_{AB}=1.67\times 10^{-9}\hat{j}N$

$\therefore$ Net force on particle $A$

$\vec{F}={\vec{F}}_{AC}+{\vec{F}}_{AB}$

$=1.67\times 10^{-9}(\hat{i}+\hat{j})N$