Question

The figure shows four arrangements of three particles of equal masses. Rank the arrangement according to the magnitude of the net gravitational force on the particle $m$, greatest first.

• A. $2,3,4,1$
• B. $1,4,3,2$
  
• C. $1$,tie of $2$ and $4$, then $3$
• D. $4,3,1,2$

Answer 1

The correct option is C $1$,tie of $2$ and $4$, then $3$

Force in $\left(i\right)$ case $=G{m}^2(\frac{1}{d^2}+\frac{1}{D^2})$

Force in $\left(iii\right)$ case $=G{m}^2(\frac{1}{d^2}-\frac{1}{(D-d{)}^2})$

Force in $\left(ii\right)$ case $=G{m}^2\sqrt{(\frac{1}{d^2}+\frac{1}{D_2})}$

Force in $\left(iv\right)$ case$=G{m}^2\sqrt{(\frac{1}{d^2}+\frac{1}{D_2})}$

$\therefore$ Decreasing order is $\left(i\right),\left(ii\right)=\left(iv\right)\left(iii\right)$
Hence, final answer is (a).