A thin rod of length $L$ is bent to form a semicircle. The mass of rod is $M.$ What will be the gravitational potential at the centre of the circle?
$-\frac {GM}{L}$
$ - \frac{{GM}}{{2\pi L}}$
$ - \frac{{\pi GM}}{{2L}}$
$ - \frac{{\pi GM}}{{L}}$
The escape velocity from a planet is $V_e.$ A tunnel is dug along the diameter of the planet and a small body dropped into it. The speed of the body at the centre of the planet will be
The change in the value of $‘g’$ at a height $‘h’$ above the surface of the earth is the same as at a depth $‘d’$ below the surface of earth. When both $‘d’$ and $‘h’$ are much smaller than the radius of earth, then which one of the following is correct?
The masses and radii of the earth and the moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are distance $d$ apart. The minimum speed with which particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is
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,
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