A particle of mass $m$ is placed at the centre of a uniform spherical shell of mass $3\,m$ and radius $R$. The gravitational potential on the surface of the shell is
$ - \frac{{Gm}}{R}$
$ - \frac{{3Gm}}{R}$
$ - \frac{{4Gm}}{R}$
$ - \frac{{2Gm}}{R}$
A spherical part of radius $R/2$ is excavated from the asteroid of mass $M$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
A body of mass $m$ is situated at a distance equal to $2R$ ($R-$ radius of earth) from earth's surface. The minimum energy required to be given to the body so that it may escape out of earth's gravitational field will be
The two planets have radii $r_1$ and $r_2$ and their densities $p_1$ and $p_2$ respectively. The ratio of acceleration due to gravity on them will be
A satellite of mass $m$ is at a distance $a$ from $a$ star of mass $M$. The speed of satellite is $u$. Suppose the law of universal gravity is $F = - G\frac{{Mm}}{{{r^{2.1}}}}$ instead of $F = - G\frac{{Mm}}{{{r^2}}}$, find the speed of the statellite when it is at $a$ distance $b$ from the star.
A projectile is projected with velocity $k{v_e}$ in vertically upward direction from the ground into the space. (${v_e}$ is escape velocity and $k < 1)$. If air resistance is considered to be negligible then the maximum height from the centre of earth to which it can go, will be : (R = radius of earth)