Gravitation practice · Easy

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

Assertion: Earth does not retain hydrogen molecules and helium atoms in its atmosphere, but does retain much heavier molecules, such as oxygen and nitrogen.
Reason: Lighter molecules in the atmosphere have translational speed that is greater or closer to escape speed of earth.

The ratio of the accelerations due gravity on two planets $P_1 \& P_2$ is $k_1$. The ratio of their respective radii is $k_2$. The ratio of their respective escape velocities is

The acceleration due to gravity on a planet is same as that on earth and its radius is 16 times that of earth. What will be the value of escape velocity on that planet if it is ${V_e}$ on earth.

A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be

Statement-1: For the planets orbiting around the sun, angular speed, linear speed, KE change with time, but angular momentum remains constant.
Statement-2: No external torque is acting on the rotating planet. So its angular momentum is constant.

Statement-1: A spherical shell produces no gravitational field anywhere.
Statement-2: The field due to various mass elements cancels out, everywhere inside and outside the shell.

Assertion: Kepler's second law can be understood by conservation of angular momentum principle
Reason: Kepler's second law is related with areal velocity which can further be proved to be based on conservation of angular momentum as $(d A / d t)=\left(r^2 \omega\right)/2$

Two electrons are revolving around a nucleus at distances ' $r$ ' and ' $4 r$ '. The ratio of their periods is

Assertion: The value of acceleration due to gravity does not depend upon mass of the body
Reason: Acceleration due to gravity is a constant quantity

The areal velocity of a planet of mass 10 kg is $15\,{m^2}/s$ it angular momentum is $\left[ {\mathrm{in}\,\,Kg\,{m^2}/s} \right]$

For a geostationary satellite the angular speed in units of radian per minute is

Statement-1: Period of revolution of satellite in circular orbit around earth is inversely proportional to its orbital speed.
Statement-2: Period of revolution in uniform circular motion is given by $T=\frac{2 \pi r}{v}$ where $r$ is radius of orbit and $v$ is speed.

If the earth is at one-fourth of its present distance from the sun, the duration of the year will be

The distance of a geostationary satellite from the centre of the earth [Radius R= 6400 km] is nearest to

The escape velocity of a projectile from the earth is approximately

The escape velocity of a particle from the surface of the earth is given by

Assertion: When a planet moves in elliptical orbit around sun, its angular momentum about sun remains conserved.
Reason: Total energy of the planet remains conserved

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

Assertion: Satellite is put in an orbit at a height where air resistance is present, then orbital velocity of the satellite will decrease.
Reason: Due to air resistance a lot of heat will be produced which may burn satellite

According to Newton's law of gravitation, the magnitude of the force $F$ on point masses $m_1$ and $m_2$ (say) is given by $|F|=\frac{G m_1 m_2}{r^2}$.
I. This equation is not directly applicable for the gravitational force between extended object (like the earth) and a point mass.
II. This equation can be applied to find the gravitational force between an extended object and a point mass provided $r$ is the distance of the point mass from the geometric centre of the extended objects.
Which of the following statement(s) about this equation is/are correct?

Given mass of the moon is $\frac{1}{{64}}$ of the mass of the earth and corresponding radius is $\frac{1}{{16}}$ of the earth. If the escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is [km/s]

Statement-1: The gravitational field intensity on the surface of the sphere is $E=\frac{G M}{R^2}$
Statement-2: The gravitational potential on the surface of the sphere is $V=\frac{-G M}{R}$.

The mass of a space ship is 500 kg. It is to be launched from the earth’s surface out into free space. The value of ‘$g$’ and ‘$R$’ (radius of earth) are $10\,m{s^{ - 2}}$ and 6400 km respectively. The required energy for this work will be [in Joules]

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

Statement-1: The force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it is zero.
Statement-2: The gravitation field due to the shell inside the shell will be zero.

Compute the additional velocity required by a satellite orbiting around earth with radius $2 R$ to become free from earth's gravitational field. Mass of earth is $M$.

If the gravitational force between two objects were proportional to $1 / R$ (and not as $1 / R^2$ ) where $R$ is separation between them, then a particle in circular orbit under such a force would have its orbital speed $v$ proportional to

Statement-1: The angular momentum under a central force is constant.
Statement-2: A force directed towards a fixed point following inverse square law is conservative

When we move from equator to pole, the value of acceleration due to gravity(g)