The two planets have radii $r_1$ and $r_2$ and their densities $p_1$ and $p_2$ respectively. The ratio of acceleration due to gravity on them will be
$r_1 p_1 : r_2 p_2$
$r_1 p_1^2 : r_2 p_2^2$
$r_1^2 p_1 : r_2^2 p_2$
$r_1 p_2 : r_2 p_1$
The condition for a uniform spherical mass m of radius r to be a black hole is [ $G$ = gravitational constant and $g$ = acceleration due to gravity]
The minimum and maximum distances of a planet revolving around the Sun are $x_{1}$ and $x_{2}$. If the minimum speed of the planet on its trajectory is $v_o$ then its maximum speed will be
The masses and radii of the earth and the moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are distance $d$ apart. The minimum speed with which particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is
The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L.$ If the distance is increased to $4r$ then the new angular momentum will be
A rocket is projected in the vertically upwards direction with a velocity kve where $v_e$ is escape velocity and $k < 1$. The distance from the centre of earth upto which the rocket will reach, will be