A geostationary satellite is orbiting the earth at a height of $6\,R$ above the surface of earth ($R$ is the radius of earth). The time period of another satellite at a height of $2.5\,R$ from the surface of the earth is :-
$3 \sqrt 2 \,hour$
$6 \sqrt 2\, hour$
$6\, hour$
$72\, hour$
The dependence of acceleration due to gravity $'g'$ on the distance $'r'$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density is as shown in figure below
If the gravitational acceleration at surface of Earth is $g$, then increase in potential energy in lifting an object of mass $m$ to a height equal to half of radius of earth from surface will be
Two planets move around the sun. The periodic times and the mean radii of the orbits are ${T_1},\,{T_2}$ and ${r_1},\,{r_2}$ respectively. The ratio ${T_1}/{T_2}$ is equal to
A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
A clock $S$ is based on oscillation of a spring and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius