Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$, then,
$T^2 \propto R^2$
$T^2 \propto R^{7/2}$
$T^2 \propto R^{3/2}$
$T^2 \propto R^{3.75}$
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
The rotation of the earth having $R$ radius about its axis speeds up to a value such that a man at latitude angle $60^o$ feels weightlessness. The duration of the day in such a case 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
The mass of planet is $\frac{1}{9}$ of the mass of the earth and its radius is half that of the earth. If a body weight $9\,N$ on the earth. Its weight on the planet would be ........ $N$
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