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

The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10 R$,where $R$ is the radius of the earth,may be described in terms of escape velocity $v_{e}$ such that $v_{i} = \sqrt{\frac{x}{y}} \times v_{e}$. The value of $x$ will be ...... .

Let the escape velocity of a body kept at the surface of a planet be $u$. If it is projected at a speed of $200 \%$ more than the escape speed,then its speed in interstellar space will be ...........

The escape velocity of a body from the Earth is $11.2 \,km/s$. If the radius of a planet is one-third the radius of the Earth and its mass is one-sixth that of the Earth, the escape velocity from the planet is: (in $\,km/s$)

The least velocity required to throw a body away from the surface of a planet so that it may not return is (radius of the planet is $6.4 \times 10^6 \ m$,$g = 9.8 \ m/s^2$).

$A$ body is projected from the earth's surface with thrice the escape velocity. What will be its velocity when it escapes the gravitational pull?