Earth has mass $M_{1}$ and radius $R_{1}$. Moon has mass $M_{2}$ and radius $R_{2}$. The distance between their centres is $r$. $A$ body of mass $M$ is placed on the line joining them at a distance $r/3$ from the centre of the Earth. To project the mass $M$ to escape to infinity,the minimum speed required is:

• A
  $\left[\frac{6 G}{r}\left(M_{1}-\frac{M_{2}}{2}\right)\right]^{\frac{1}{2}}$
• B
  $\left[\frac{6 G}{r}\left(M_{1}+\frac{M_{2}}{2}\right)\right]^{\frac{1}{2}}$
• C
  $\left[\frac{3 G}{r}\left(M_{1}+\frac{M_{2}}{2}\right)\right]^{\frac{1}{2}}$
• D
  $\left[\frac{3 G}{r}\left(M_{1}-\frac{M_{2}}{2}\right)\right]^{\frac{1}{2}}$