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)
$\frac{R}{{{k^2} + 1}}$
$\frac{R}{{{k^2} - 1}}$
$\frac{R}{{1 - {k^2}}}$
$\frac{R}{{k + 1}}$
A geo-stationary satellite is orbiting the earth at a height of $6 R$ above the surface of earth, $R$ being the radius of earth. The time period of another satellite at a height of $2.5 R$ from the surface of earth is
A particle of mass $m$ is placed at the centre of a uniform spherical shell of mass $3\,m$ and radius $R$. The gravitational potential on the surface of the shell is
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac {a}{2}$ distance from the centre, will be
A geostationary satellite is orbiting the earth at a height of $6\, R$ from the earth’s surface ($R$ is the earth’s radius ). What is the period of rotation of another satellite at a height of $2.5\, R$ from the earth’s surface
Radius of the earth is $R$. If a body is taken to a height $3R$ from the surface of the earth than change in potential energy will be