Two planets A and B have identical radii but different densities, $\rho_A$ and $\rho_B$, respectively, where $\rho_A = 2\rho_B$. The ratio of their escape velocities, $v_A/v_B$, is:

A particle of mass m is moving in a horizontal circle of radius r,under a centripetal force $= \frac{k}{{{r^2}'}}\;{\rm{where\;}}k{\rm{\;is\;a\;constant}}.$

If M = mass of the earth, R = radius of the earth, then what is the gravitational potential at a distance $r = \frac{R}{2}$ from its centre? (Consider gravitational potential at infinite is zero)

The escape velocity from a planet's surface is independent of which of the following?

Escape speed of a body from the earth depend on

If $v_e$ is escape speed from the Earth and $v_p$ is that from a planet of half the radius of Earth, then:

Infinite number of masses, each 1 kg, are placed along the $x$-axis at $x = \pm 1{\rm{m}},{\rm{\;}} \pm 2{\rm{m}},{\rm{\;}} \pm 4{\rm{m}},{\rm{\;}} \pm 8{\rm{m}},{\rm{\;}} \pm 16{\rm{m}}$ ….. The magnitude of the resultant gravitational potential in terms of gravitational constant $G$ at the origin ($x = 0$) is

Assertion: Earth does not retain hydrogen molecules and helium atoms in its atmosphere, but does retain much heavier molecules, such as oxygen and nitrogen.Reason: Lighter molecules in the atmosphere have translational speed that is greater or closer to escape speed of earth.

A planet of mass of $\frac{1}{6}$ th of earth's mass, radius of $\frac{1}{3}$ rd of earth's radius. If escape speed for earth is $11.2 \mathrm{~km} / \mathrm{s}$, then escape speed for the planet shall be $\mathrm{km} / \mathrm{s}$ (nearest integer).

The escape velocity for a planet is $v_e$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

The ratio of orbital velocity of an earth's satellite to the escape velocity of the same earth's satellite is very nearly equal to