A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)
$\frac{R}{{{k^2} + 1}}$
$\frac{R}{{{k^2} - 1}}$
$\frac{R}{{1 - {k^2}}}$
$\frac{R}{{k + 1}}$
The kinetic energy needed to project a body of mass $m$ from the earth's surface (radius $R$ ) to infinity is
If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is
A body tied to a string of length $L$ is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range $AC$ of the body will be
The potential energy of a satellite of mass $m$ and revolving at a height $R_e$ above the surface of earth where $R_e =$ radius of earth, is
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then