When the total energy of a satellite-planet system is positive,the satellite will .......

$A$ body of mass $m$ is projected with velocity $\lambda v_{e}$ in a vertically upward direction from the surface of the earth into space. It is given that $v_{e}$ is the escape velocity and $\lambda < 1$. If air resistance is considered to be negligible,then the maximum height from the center of the earth,to which the body can go,will be: ($R$: radius of earth)

The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then the ratio of the escape velocities from the planets is

The escape velocity for the earth is $v_e$. The escape velocity for a planet whose radius is four times and density is nine times that of the earth,is (in $,v_e$)

An object $A$ of mass '$m$' is located at a point '$P$' at distances '$r$' and '$2r$' from two planets $B$ and $C$ of masses '$M$' and '$6M$' respectively,as shown in the figure. If the escape speed of the object $A$ from point '$P$' due to the gravitational influence of only planet $B$ is $5 \ km/s$,then the escape speed of the object $A$ from point '$P$' due to the gravitational influence of both the planets is . . . . . . $km/s$.

$A$ very small groove is made in the earth,and a particle of mass $m_0$ is placed at $\frac{R}{2}$ distance from the centre. Find the escape speed of the particle from that place.