The escape velocity for the earth is $11.2 \ km/s$. The mass of another planet is $100$ times that of the earth and its radius is $4$ times that of the earth. The escape velocity for this planet will be ......... $km/s$.

Explain escape speed. On what factors does escape velocity not depend?

$A$ rocket is launched normal to the surface of the Earth,away from the Sun,along the line joining the Sun and the Earth. The Sun is $3 \times 10^5$ times heavier than the Earth and is at a distance $2.5 \times 10^4$ times larger than the radius of the Earth. The escape velocity from the Earth's gravitational field is $v_e = 11.2 \text{ km s}^{-1}$. The minimum initial velocity $(v_s)$ required for the rocket to be able to leave the Sun-Earth system is closest to:
(Ignore the rotation and revolution of the Earth and the presence of any other planet)

There are two planets. The ratio of the radii of the two planets is $K$,and the ratio of the acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocities?

$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)