Earth has mass ' $\mathrm{M}_{1}{ }^{\prime}$ and Radius ' $\mathrm{R}_{1}{ }^{\prime}$. Moon has mass ${…
Earth has mass ' $\mathrm{M}_{1}{ }^{\prime}$ and Radius ' $\mathrm{R}_{1}{ }^{\prime}$. Moon has mass ${ }^{\prime} \mathrm{M}_{2}{ }^{\prime}$ and radius ${ }^{\prime} \mathrm{R}_{2}{ }^{\prime}$. Distance
between their centres is ' $\mathrm{r}^{\prime}$. A body of mass ' $\mathrm{M}^{\prime}$ is placed on the line joining them
ata distance $\frac{\mathrm{r}}{3}$ from centre of the earth. To project the mass ' $\mathrm{M}^{\prime}$ to escape to infinity,
the minimum speed required is
The binding energy of the body is given by
$\text { B.E. } \begin{aligned}
&=\frac{G M_{1} M}{\frac{r}{3}}+\frac{G M_{2} M}{\frac{2 r}{3}} \\
&=\frac{3 G M_{1} M}{r}+\frac{3 G M_{2} M}{2 r} \\
&=\frac{3 G M}{r}\left[M_{1}+\frac{M_{2}}{2}\right]
\end{aligned}$
If $V$ is the velocity given to the body, then
$\begin{aligned}
& \frac{1}{2} m V^{2}=\frac{3 G M}{r}\left[M_{1}+\frac{M_{2}}{2}\right] \\
\therefore \quad & V=\left[\frac{6 G}{r}\left(M_{1}+\frac{M_{2}}{2}\right)\right]^{\frac{1}{2}}
\end{aligned}$