The potential energy of a satellite is $-8 \times 10^9 \ J$. What is its binding energy (escape energy)?

The mass and radius of the earth and moon are $M, R$ and $m, r$ respectively. The distance between their centers is $d$. The minimum velocity with which a particle of mass $m_0$ should be projected from the midpoint between them so that it could reach infinity is

The escape velocity for a planet is $v_e$. $A$ tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet,its speed will be

If $M$ is the mass of a planet and $R$ is its radius,then in order to become a black hole (where $c$ is the speed of light),which condition must be satisfied?

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

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 $\,km/s$)