The acceleration due to gravity on a planet is the same as that on Earth,and its radius is four times that of Earth. What will be the value of the escape velocity on that planet if it is $v_e$ on Earth?

If the radius of a planet is $R$ and its density is $\rho$,the escape velocity from its surface will be

The escape velocity from the surface of the Earth is $V_e$. The escape velocity from the surface of a planet whose mass and radius are $3$ times those of the Earth will be:

$A$ body is projected vertically upwards from the Earth's surface. If the velocity of projection is $\left(\frac{1}{3}\right)$ of the escape velocity,then the height up to which the body rises is $(R = \text{radius of Earth})$

$A$ rocket has to be launched from the Earth in such a way that it never returns. If $E$ is the minimum energy delivered by the rocket launcher,what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the Moon? Assume that the density of the Earth and the Moon are equal and that the Earth's volume is $64$ times the volume of the Moon.

There is no atmosphere on the moon because