Escape Velocity

Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity  $\frac{{\text{V}}_{\text{A}}}{{\text{V}}_{\text{B}}}\text{is}$

A missile is launched with a velocity less than the escape velocity. The sum of kinetic energy and potential energy is :

The escape velocity on the surface of the moon is small because moon has a less surface _____.
 

The escape velocity on the moon is less than that on the earth.

There's no atmosphere on the moon. Why?

Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11}\mathit{ }g,$ where $g$ is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $1.5$ times that of the earth. If the escape speed on the surface of the earth is taken to be $11 \mathrm{km} {\mathrm{s}}^{-1}$ the escape speed on the surface of the planet in $\mathrm{km} {\mathrm{s}}^{-1}$ will be

Two bodies each of mass $M$ are kept fixed with a separation $2L$. A particle of mass $m$ is projected from the mid-point of the line joining their centres perpendicular to the line. The gravitational constant is $G$. The correct statement $\left(s\right)$ is (are)

The escape velocity of a spherical planet of radius $R$ and density $\rho$ is $V$. If the radius of this planet is changed to $3R$ and density is changed to $3\rho$, then the escape velocity of the planet will be changed to

Compare the escape velocities of earth and moon.

What is the reason behind the moon having no atmosphere?

Velocity of escape, from earth’s surface, is _____  $\mathrm{km} {\mathrm{s}}^{-1}$.

Calculate the escape velocity of a body from the surface of the earth. $(\mathrm{Given}: G=6.67 \mathrm{x} {10}^{-11} {\mathrm{Nm}}^2/{\mathrm{kg}}^2, R=6400 \mathrm{km}, g=9.8 \mathrm{m}/{\mathrm{s}}^2)$

Define escape velocity. Write an expression for the escape velocity of an object from the surface of the earth.

If any object is thrown upwards with a velocity more than $11.2 \mathrm{km}/\sec$, then the object will:

Gravitational acceleration on the surface of the planet is $\frac{\sqrt{6}}{11}g$, where $g$ is the acceleration due to gravity on the surface of earth. The average mass density of the planet is $\frac{2}{3}$ times that of the earth. If the escape speed on the surface of the earth is taken to be $11 \mathrm{k}\mathrm{m} {\mathrm{s}}^{-1}$, then find the escape speed on the surface of the planet (in $\mathrm{k}\mathrm{m} {\mathrm{s}}^{-1}$).

Velocity of escape is _____ times the orbital velocity of a satellite revolving very close to the surface of earth. 
(Choose from $\sqrt{3} (1.732)$ or $\sqrt{2} (1.414)$.)

Choose the incorrect statements from the following options.

An unmanned satellite $A$ and a spacecraft $B$ are orbiting around the earth in the same circular orbit as shown. The spacecraft is ahead of the satellite by some time. Let us consider that some technical problem has arisen in the satellite and the astronaut from $B$ has made it correct. For this to be done docking of two ($A$ and $B$) is required (in layman terms connecting $A$ and $B$). To achieve this, the rockets of $A$ have been fired in the forward direction and docking takes place as shown in the figure below

Take the mass of the earth $=5.98\times {10}^{24} \mathrm{k}\mathrm{g}$
The radius of the earth $=6400 \mathrm{k}\mathrm{m}$
Orbital radius $=9600 \mathrm{k}\mathrm{m}$
Mass of satellite $A=320 \mathrm{k}\mathrm{g}$
Mass of spacecraft $B=3200 \mathrm{k}\mathrm{g}$
Assume that initially, spacecraft $B$ leads satellite $A$ by $100 \mathrm{s}$, i.e., A arrives at any particular position after $100 \mathrm{s}$ of $B\text{'}\mathrm{s}$ arrival. Based on the above information answer the following question.
If from the base station, the rocket system of $A$ has been operated, so that its rocket has been fired in forward direction thus reducing the speed of $A$ by $0.5\mathrm{\%}$, then which of the following will happen?

A satellite is revolving at a height $h$ from the surface of earth. Then the change in velocity for the satellite to escape the gravitational field of earth, is:

There are two identical starts of mass $3\times {10}^{31} kg$ each with distance $2\times {10}^{11}m$ between them. Now a material is projected with velocity $v$ from the midpoint of the line joining the stars. What should be the minimum value of $v$ so that it goes out by gravitational field of the given stars?