Physics - Gravitation Question with Solution | TestHub

Let at $O$ there will be a collision. If smaller sphere moves $x$ distance to reach at $O$, then bigger sphere will move a distance of $(9R-x)$.$\begin{array}{rl}F& =\frac{GM\times 5M}{(12R-x{)}^2}\\ a_{\text{small }}& =\frac{F}{M}=\frac{G\times 5M}{(12R-x{)}^2}\\ a_{\mathrm{big}}& =\frac{F}{5M}=\frac{GM}{(12R-x{)}^2}\\ x& =\frac{1}{2}{a}_{\text{small }}{t}^2=\frac{1}{2}\frac{G\times 5M}{(12R-x{)}^2}{t}^2\dots (i)\\ (9R-x)& =\frac{1}{2}{a}_{\text{big }}{t}^2=\frac{1}{2}\frac{GM}{(12R-x{)}^2}{t}^2\dots (ii)\end{array}$ Thus, dividing Eq. (i) by Eq. (ii), we get $\frac{x}{9R-x}=5$ $\begin{array}{rl}& \Rightarrow x=45R-5x\\ & \Rightarrow 6x=45R\\ & \therefore x=7.5R\\ & \end{array}$