Gravitation practice · Mixed difficulty

Which of the following quantities does not depend upon the orbital radius of a satellite? (Take, $R=$ radius of orbit)

Two bodies of masses $100kg$ and $10,000\,\,kg$ are at a distance of $1m$ apart. At what distance from $100kg$ on the line joining them will the resultant gravitational field intensity be zero.

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (Where $g$ is the acceleration due to gravity on the surface of the earth) in terms of the radius of the earth R is

A satellite with kinetic energy ${E_k}$ is revolving round the earth in a circular orbit. How much more kinetic energy should be given to it so that it may just escape into outer space

If the earth were made of lead of relative density 11.3, what then would be the value of acceleration due to gravity on the surface of the earth? Radius of the earth $=6.4 \times 10^6 \mathrm{~m}$ and ${G}=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$.

The earth is an approximately sphere. If the
interior contained matter which is not of the
same density everywhere, then on the surface
of the earth, the acceleration due to gravity:

A point mass $m$ is placed inside a spherical shell of radius R and mass $M$. at a distance $\frac{R}{2}$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is

Statement-1: There is almost no effect of rotation of earth at poles.
Statement-2: Because rotation of earth is about polar axis.

Two planets have the same average density but their radii are ${R_1}\,and\,{R_2}$. If acceleration due to gravity on these planets be ${g_1}\,and\,{g_2}$ respectively, then

Kepler’s second law states that the straight line joining the planet to the sun sweeps out equal times. This statement is equivalent to saying that

Earth is flattened at poles, bulged at the equator. This is due to:

Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3V, the speed of the satellite B will be

Centripetal acceleration is

Weightlessness experienced while orbiting the Earth in space-ship, is the result of:

Assertion: The time period of revolution of a satellite close to surface of earth is smaller than that revolving far from surface of earth.
Reason: The square of time period of revolution of a satellite is directly proportional to cube of its orbital radius.

Force between two objects of equal masses is $F$. If $25 \%$ mass of one object is transferred to the other object, then the new force will be

Assertion: If gravitational force is proportional to $\frac{1}{\mathrm{R}^3}$ then Keplar's second law would not be affected.
Reason: For Keplar's second law, central nature of force is the only condition.

A satellite is moving in a circular orbit round the earth with a diameter of orbit $2 R$. At a certain point a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially. The resulting orbit of the satellite would be

The gravitational force between two bodies of masses 2 kg and 8 kg is $6.67 \times {10^{ - 11}}N.$ Find the distance between two bodies $\left[ {G = 6.67 \times {{10}^{ - 11}}\,N{m^2}/k{g^2}} \right]$ is

A satellite of mass $m$ is circulating around the earth with constant angular velocity. If the radius is $R_0$ and mass of earth is $M$, then the angular momentum about the centre of the earth is

The centripetal force acting on a satellite orbiting round the earth and the gravitational force of earth acting on the satellite both equal $F$. The net force on the satellite is

A planet is revolving round the sun in an elliptical orbit, If $\mathbf{v}$ is the velocity of the planet when its position vector from the sun is $\mathbf{r}$, then areal velocity of the planet is

Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon

If gravitational constant is decreasing with time, what will remain unchanged in case of a satellite orbiting around earth

The height from the surface of earth at which the gravitational potential energy of a ball of mass $m$ is half of that at the centre of earth is (where $R$ is the radius of earth)

When a body is lifted from surface of earth at a height equal to radius of earth, then the change in its potential energy is

A body of mass $m$ is taken from earth surface to the height $\mathrm{h}$ equal to radius of earth, the increase in potential energy will be

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct

Assertion: Space ship while entering the Earth’s atmosphere is likely to catch fire.
Reason: Temperature of upper atmosphere is very high.

The ratio of gravitational force and electrostatic repulsive force between two electrons is approximately (gravitational constant $=6.7 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2,$ mass of an electron $=9.1 \times 10^{-31} \mathrm{~kg},$ charge on an electron $=1.6 \times 10^{-19} \mathrm{C}$)