For an object projected from the Earth,on which two factors does the escape velocity $NOT$ depend?

$A$ particle is projected vertically up with velocity $v = \sqrt{\frac{4 g R_e}{3}}$ from the Earth's surface. The velocity of the particle at a height equal to half of the maximum height reached by it is .........

If the radius of a planet is four times that of Earth and the value of $g$ is the same for both,the escape velocity on the planet will be ......... $km/s$.

$A$ particle falls towards the Earth from infinity. Its velocity on reaching the Earth would be:

$A$ very small groove is made in the earth,and a particle of mass $m_0$ is placed at $\frac{R}{2}$ distance from the centre. Find the escape speed of the particle from that place.

The escape velocity on Earth is $11.2 \, km/s$. On another planet having twice the radius and $8$ times the mass of the Earth,the escape velocity will be ......... $km/s$.