Escape Velocity

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

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.

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.

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?

The ratio of accelerations due to gravity $g_1 : g_2$ on the surfaces of two planets is $5 :2$ and the ratio of their respective average densities ${\rho }_1:{\rho }_2$ is $2 :1$ . What is the ratio of respective escape velocities $v_1 :v_2$ from the surface of the planets?

The escapse velocity from the Earth is $11 km{s}^{-1}.$ The escpe velocity from a planet having twice the radius and same mean density as that of Earth is

The escape velocity from the earth is about $11 km{s}^{-1}$ . The escape velocity from a planet having twice the radius and the same mean density as the earth is

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

Escape velocity at surface of earth is $11.2 \mathrm{km}/\mathrm{s}$. Escape velocity from a planet whose mass is the same as that of earth and radius $1/4$ that of earth, is

The escape velocity on the surface of earth is 11.2 km/s. What would be the escape velocity on the surface of another planet of the same mass but $\frac{1}{4}$ times the radius of the earth?

The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

The value of escape velocity of a certain planet is 2 km/s. Then the value of orbital speed for a satellite orbiting closer to its surface is:

There is no atmosphere on the moon because

Two spherical planets P and Q have the same uniform density $\rho$ , masses $M_P$ and $M_Q$ , and surface areas A and 4A, respectively. A spherical planet R also has uniform density $\rho$ and its mass is $\left(M_P+M_Q\right)$ . The escape velocities from the planets P, Q and R, are $v_P$ , $v_Q$ , $v_R$ respectively, then