Escape Velocity — MCQ Practice

The escape velocity from the surface of Earth is $v_e$. The escape velocity from the surface of a planet whose radius is four times that of Earth and mass is 16 times that of Earth will be:

If the acceleration due to gravity on the surface of a planet is $g_P$ and its radius is $R_P$, then the escape velocity from its surface is:

An object of mass $m$ is projected from the surface of a planet of mass $M$ and radius $R$ with a velocity $v = 2v_e$, where $v_e$ is the escape velocity. What will be its velocity when it is at a very large distance from the planet?

The ratio of escape velocity on Earth ($v_E$) to the escape velocity on the Moon ($v_M$) is approximately (Given: Mass of Earth $M_E = 81 M_M$, Radius of Earth $R_E = 4 R_M$)

The escape velocity from Earth's surface is $11.2\,\text{km/s}$. A body is projected with a velocity $22.4\,\text{km/s}$. What is the velocity of the body at infinite distance from Earth?

If a planet has a mass $M$ and radius $R$, and its density is uniform, how does its escape velocity depend on its radius $R$?

What is the minimum energy required to launch a satellite of mass $m$ from the surface of Earth (mass $M$, radius $R$) to an infinite distance?