The orbital velocity of an artificial satellite in a circular orbit very close to earth is $v$. The velocity of a geo-stationary satellite orbiting in circular orbit at an altitude of $3R$ from earth's surface will be
$\frac{v}{{\sqrt 7 }}$
$\frac{v}{{\sqrt 6 }}$
$\frac{v}{2}$
$\frac{v}{{\sqrt 2 }}$
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
A satellite is launched into a circular orbit of radius $R$ around earth, while a second satellite is launched into a circular orbit of radius $1.02\, {R}$. The percentage difference in the time periods of the two satellites is -
The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?
The force of gravitation is
A spherical part of radius $R/2$ is excavated from the asteroid of mass $M$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is