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 whichit 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 escape velocity for a body projected vertically upwards from the surface of earth is $11\, km/s$. If the body is projected at an angle of $45^o$ with the vertical, the escape velocity will be ........... $km/s$
Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitationalforce will now be
A planet orbits the sun in an elliptical path as shown in the figure. Let $v_P$ and $v_A$ be speed of the planet when at perihelion and aphelion respectively. Which of the following relations is correct ?
A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{{dM}}{{dt}} = \alpha v$ where $M$ is the mass (of satellite + dust) at that instant . The instantaneous acceleration of the satellite is