Question

What is the net force on a ball of mass m placed between two balls of same masses m at a distance $\frac{r}{4}$ from one ball :

• A. $\frac{9G{m}^2}{128r^2}$
• B. $\frac{9G{m}^2}{32r^2}$
• C. $\frac{64G{m}^2}{9r^2}$
• D. $\frac{128G{m}^2}{9r^2}$

Answer 1

The correct option is D $\frac{128G{m}^2}{9r^2}$

$F_{21}=\frac{G{m}_1{m}_2}{(r/4{)}^2}=\frac{16G{m}_1{m}_2}{r^2}$ ………….$\left(1\right)$

$F_{31}=\frac{G{m}_1{m}_3}{(r-r/4{)}^2}=\frac{G{m}_1{m}_2}{9r^2/16}$

$F_{31}=\frac{16G{m}_1{m}_3}{9r^2}$ …………$\left(2\right)$

$F_{Net}=F_{21}-F_{31}=\frac{16G{m}_1{m}_2}{r^2}-\frac{16G{m}_1{m}_2}{9r^2}$

$=\frac{16G{m}^2}{r^2}[1-\frac{1}{9}]=\frac{128G{m}^2}{9r^2}$.