Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then, the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
$R^n$
${R^{\left( {n + 1} \right)/2}}$
${R^{\left( {n - 1} \right)/2}}$
$R^{-n}$
If the change in the value of ' $g$ ' at a height ' $h$ ' above the surface of the earth is same as at a depth $x$ below it, then ( $x$ and $h$ being much smaller than the radius of the earth)
A mass $m$ , travelling at speed $V_0$ in a straight line from far away is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$ , the distance of closest approach between the mass and the black hole is given by the relation
Starting from the centre of the earth having radius $R,$ the variation of $g$ (acceleration due to gravity) is shown by
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be
A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )