In a certain region of space, the gravitational field is given by $-k/r$ , where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r = r_0$ be $V_0$ , then what is the expression for the gravitational potential $(V)$ ?
$k\,log\,(r/r_0)$
$k\,log\,(r_0/r)$
$V_0\, +\, k\, log\, (r/r_0)$
$V_0\, +\, k\, log\, (r_0/r)$
Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere)
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
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]
Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$ )?