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,
$T^2 \propto R^2$
$T^2 \propto R^{7/2}$
$T^2 \propto R^{3/2}$
$T^2 \propto R^{3.75}$
According to Kepler’s law the time period of a satellite varies with its radius as
A satellite is orbitting around the earth with areal speed $v_a$. At what height from the surface of the earth, it is rotating, if the radius of earth is $R$
If the radius of earth shrinks by $1.5 \%$ (mass remaining same), then the value of gravitational acceleration changes by ......... $\%$
Which of the following statements are true about acceleration due to gravity?
$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$
$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$
$(c)\,\,'g'$ is zero at the centre of earth
$(d)\,\,'g'$ decreases if earth stops rotating on its axis
A satellite is moving around the earth with speed $V$ in circular orbit of radius $r$ . If the orbital radius is decreased by $2\%$ , the speed of the satellite will