Gravitation practice · Medium

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

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.

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

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

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

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 $=1.6 \times 10^{-19} \mathrm{C}$)

A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

Time period of revolution of a nearest satellite around a planet of radius $R$ is $T$. Period of revolution around another planet, whose radius is $4 R$ but having same density is

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of earth of radius $R$. If $r < R$, then

The gravitational field at some point in space is $\overrightarrow g = 8\hat i + 6\hat j\,N/kg$. The force exerted on a 1 kg mass placed at that point is

If mass of a satellite is doubled and time period remain constant the ratio of orbit in the two cases will be

The correct option is

A uniform spherical shell gradually shrink maintaining its shape. The gravitational potential at its centre will (Mass of the shell remains same)

A body is projected vertically upwards from the surface of the earth with a speed equal to $\frac{1}{4}$th of escape velocity from surface of earth. Maximum height attained by the body from the surface of the earth will be ($R$-Radius of earth)

The angular speed with which earth should spin about its axis, such that a person feels $\left(\frac{5}{9}\right)^{\text {th}}$ times his weight at equator as compared to his weight at pole