Gravitation practice · Medium

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 $km/s$ )

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

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

Every planet revolves around the sun in an elliptical
orbit:

A. The force acting on a planet is inversely
proportional to square of distance from sun.

B. Force acting on planet is inversely proportional
to product of the masses of the planet and the
sun.

C. The Centripetal force acting on the planet is
directed away from the sun.

D. The square of time period of revolution of
planet around sun is directly proportional to
cube of semi-major axis of elliptical orbit.

Choose the correct answer from the options given
below:

Two identical satellites are at $R$ and $7R$ away from earth surface, the wrong statement is

Assertion: For circular orbits, the law of periods is ${T}^2 \propto {r}^3$, where ${M}$ is the mass of sun and $r$ is the radius of orbit.
Reason: The square of the period $T$ of any planet about the sun is proportional to the cube of the semi-major axis $a$ of the orbit.

A satellite of mass 200 kg is orbiting around the earth at a height of 400 km above its surface. The energy required to send it out of the earth’s gravitational influence is (Mass of earth $= 6 \times {10^{24}}kg$, Radius of earth = 6000 km, $G = 6.67 \times {10^{ - 11}}\,N{m^2}\,k{g^{ - 2}}$)

The masses and radii of the earth and moon are ${M_{1,}}{R_1}$ and ${M_{2,}}{R_2}$ respectively, their centres are distance $d$ apart. The minimum velocity with which a particle of mass $m$ should be projected from a point midway between their centres so that it escapes to infinity is

Two bodies of masses ${m_1}\,and\,{m_2}$ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance $r$ between them is

In the following four periods
(i) Time of revolution of a satellite just above the earth’s surface $\left( {{T_{st}}} \right)$ , (ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth $\left( {{T_{ma}}} \right)$ , (iii) Period of simple pendulum having a length equal to the earth’s radius in a uniform field of $9.8N/kg\left( {{T_{sp}}} \right)$ , (iv) Period of an infinite length simple pendulum in the earth’s real gravitational filed $\left( {{T_{is}}} \right)$

The ratio of orbital velocity of an earth's satellite to the escape velocity of the same earth's satellite is very nearly equal to