Physics Gravitation

Consider two solid spheres of radii ${}_{}$ $R_1=1\mathrm{m}$ , $R_2=2m$ ${}_{}$ and masses $M_1$ ${}_{}$ and $M_2$ ${}_{}$ , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M_1}{M_2}$ $\frac{{}_{}}{{}_{}}$ is:

Consider two solid spheres of radii $R_1=1\mathrm{m}$ ${}_{}$ , $R_2=2m$ ${}_{}$ and masses $M_1$ ${}_{}$ and $M_2$ ${}_{}$ , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $\frac{M_1}{M_2}$ $\frac{{}_{}}{{}_{}}$ is:

A satellite of mass $m$ $$ is launched vertically upwards with an initial speed $u$ $$ from the surface of the earth. After it reaches height $R(R=$ $$ radius of the earth), it ejects a rocket of mass $\frac{\mathrm{m}}{10}$ $\frac{}{}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( $G$ $$ is the gravitational constant ; $$ $M$ is the mass of the earth)

A box weighs $196\mathrm{N}$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}$ at the north pole and the radius of the earth $=6400\mathrm{k}\mathrm{m}$  )

The maximum and minimum distances of a comet from the Sun are 1.6 x1012m and 8.0 x1010m respectively. If the speed of the comet at the nearest point is 6x104ms-1, the speed at the farthest point is:

Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is:

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 * 10³ km. Find the mass of Mars.
{Given 4π²/G = 6 * 10¹¹ N⁻²kg²}

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is √(aGM/(7R)) then the value of 'a' is _______. [Given: The two planets are fixed in their position]

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

The minimum and maximum distances of a planet revolving around the Sun are x? and x?. If the minimum speed of the planet on its trajectory is v?, then its maximum speed will be :