Physics Gravitation

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Rₑ. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become √(3/2) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is:

The mass density of a spherical galaxy varies as K/r over a large distance 'r' from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:

A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:

The acceleration due to gravity on the earth's surface at the poles is g an and angular velocity of the earth about the axis passing through the pole is ω. An object is weight at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is : (h << R, where R is the radius of the earth)

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: