Two planets A and B have the same density but different radii. The ratio of their escape velocities is $v_{eA} : v_{eB} = 1:2$. What is the ratio of their radii $R_A : R_B$?

Two satellites $A$ and $B$ go around the earth in circular orbits at heights of $R_A$ and $R_B$ respectively from the surface of the earth. Assuming the earth to be a uniform sphere of radius ${R}_{{e}},$ the ratio of the magnitudes of their orbital velocities is:

The escape velocity of a particle of mass $m$ varies as

For a body escape velocity is $11 \mathrm{~km} / \mathrm{s}$. If the body is projected at an angle of $60^{\circ}$ with the vertical, then escape velocity will be

A spherical planet has a mass ${M_P}$ and diameter ${D_P}$. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to

How much energy will be needed for a body of mass $100 \mathrm{~kg}$ to escape from the earth$\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right.$ and radius of earth $=6.4 imes 10^6 \mathrm{~m}$ )

A planet has a radius one-third that of Earth and its mass is one-sixth that of Earth. What is the escape velocity from this planet, given that the escape velocity from Earth is 11.2 km/s?

A spherical planet of uniform density $\rho$ and radius R has a tunnel drilled through its center. An object is dropped into the tunnel. The time it takes to reach the other side of the planet is:

The escape velocity of a body from the surface of the earth is ${V_1}$ and from an altitude equal to twice the radius of the earth, is ${V_2}$. Then,

Two metallic spheres each of mass $M$ are suspended by two strings each of length $L$. The distance between the upper ends of strings is $L$. The angle which the strings will make with the vertical due to mutual attraction of the spheres is

The gravitational force between two point masses ${m_1}\,and\,{m_2}$ at separation $r$ is given by $F = k\frac{{{m_1}{m_2}}}{{{r^2}}}$. The constant $k$