Escape Velocity

Ajay can throw a ball at a speed on Earth which can cross a river of width $10 \mathrm{~m}$. Ajay reaches on an imaginary planet whose mean density is twice of the Earth. Find out the maximum possible radius of planet in $\mathrm{km}$ so that if Ajay throws the ball at same speed it may escape from planet. Given radius of Earth $=6.4 \times 10^{6} \mathrm{~m}$

Assume that a tunnel is dug across the Earth $\left(\text{radius}=R\right)$ passing through its centre. The time a particle takes to reach centre of Earth if it is projected into the tunnel from surface of Earth with speed needed for it to escape the gravitational field of Earth is ${\sin }^{-1}\left(\frac{1}{\sqrt{a}}\right)\sqrt{\frac{R_e}{g}}$. Find $a$.

A body of mass $m$ is situated at distance $4R_e$ above the earth's surface, where $R_{\mathit{e}}$ is the radius of earth how much minimum energy be given to the body so that it may escape :-

Escape velocity of a body from the surface of Earth is $11.2 \mathrm{km} {\mathrm{s}}^{-1}$. from the Earth surface. If the mass of Earth becomes double of its present mass and radius becomes half of its present radius, then escape velocity will become 

Masses and radii of earth and moon are $M_1, M_2$ and $R_1, R_2$ respectively. The distance between their centre is $d$. The minimum velocity is given to mass $M$ from the mid-point of the line joining their centre so that it will escape: