Gravitation practice · Mixed difficulty

How much below the surface of the earth does the acceleration due to gravity become $1 \%$ of its value at the earth's surface? Radius of the earth $=6400 \mathrm{~km}$.

Two bodies of masses 2kg and 8kg are separated by a distance of 9 m. the point where the resultant gravitational field intensity is zero is at a distance of

Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because

Assertion: Comets move around the Sun in elliptical orbits. The gravitational force on the comet due to Sun is not normal to the comet? Velocity but the work done by the gravitational force over every complete orbit of the comet is zero.
Reason: Gravitational force is a non-conservative force.

Select the correct statement from the following

An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will

The escape velocity from the earth is $11\,\,km/s$ . The escape velocity from a planet having twice the radius and same density as that of the earth is (in $km/s$ )

The value of acceleration due to gravity at the surface of earth

A planet of mass of $\frac{1}{6}$ th of earth's mass, radius of $\frac{1}{3}$ rd of earth's radius. If escape speed for earth is $11.2 \mathrm{~km} / \mathrm{s}$, then escape speed for the planet shall be $\mathrm{km} / \mathrm{s}$ (nearest integer).

Assertion: When two masses come closer, their gravitational potential energy decreases.

Reason: Two masses attract each other.

If the mass and radius of the planet are doubled
then acceleration due to gravity on its surface will
become (density of the planet remains same)

Assertion: Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth.
Reason: According to law of conservation of angular momentum, the plane of rotation of satellite always remains same.

If a new planet is discovered rotating around the sum with the orbital radius double that of earth, then what will be its time period (in earth’s days)?

Given below are two statements:
Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit $\left( {{E_1}} \right)$ to higher energy orbit $\left( {{E_2}} \right),$ is given as $hf = {E_1} - {E_2}.$
Statement II: The jumping of electron from higher energy orbit $\left( {{E_2}} \right)$ to lower energy orbit $\left( {{E_1}} \right)$ is associated with frequency of radiation given as $f = \frac {{\left( {{E_2} - {E_1}} \right)}}{h}.$
This condition is Bohr’s frequency condition.
In the light of the above statements, choose the correct answer from the options given below:

A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is

LANDSAT series of satellites move in near polar orbits at an altitude of

Two planets of radii in the ratio $2:3$ are made from the material of density in the ratio $3:2$. Then, the ratio of acceleration due to gravity $\frac{{{g_1}}}{{{g_2}}}$ at the surface of the two planets will be

Escape speed of a body from the earth depend on

Two spheres of radius $r\,and\,2r$ are touching each other. The fore of attraction between them is proportional to

Assertion: At pole value of acceleration due to gravity $(g)$ is greater than that of equator.

Reason : Earth rotates on its axis in addition to revolving round the sun.

${V_e}$ and ${V_p}$ denotes the escape velocity from the earth and another planet having half the radius and the same mean density as the earth then

The maximum horizontal range of a projectile on the earth is R. Then for the same velocity of projection, its maximum range on another plant is $\frac{{5R}}{4}$. Then the ratio of acceleration due to gravity on that planet and on the earth is

A satellite in a circular orbit of radius $R$ has a period of $4h$. Another satellite with orbital radius $3R$ around the same planet will have a period (in hour)

The escape velocity of a projectile from the earth is approximately

If the mass of a body is $M$ on the surface of the earth, then mass of the same body on the surface of the moon is

Statement-1: The speed of satellite always remains constant in an orbit
Statement-2: The speed of a satellite depends on its path.

The period of a satellite in a circular orbit around a planet is independent of

A satellite of the sun is in circular orbit around the sun, midway between the sun and the earth. Then

Assertion: Angular momentum of a satellite remains conserved.
Reason: Conservation of linear momentum leads to conservation of angular momentum.

The weight of a body on surface of earth is 12.6 N. When it is raised to a height half the radius of earth its weight will be