Gravitation practice · Medium

Kepler's law states that, square of the time period of any planet moving around the sun in an elliptical orbit of semi-major axis $(R)$ is directly proportional to

An object is allowed to fall from a height $R$ above the earth, where $\mathrm{R}$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

Assertion: A body kept inside a spherical shell does not experience any gravitational force.
Reason: The body inside a spherical shell is protected from the gravitational attraction of bodies outside the shell.

A satellite of mass $m$ moves along an elliptical path around earth. Its areal velocity is

Assertion: The universal gravitational constant is same as acceleration due to gravity.
Reason: Gravitational constant and acceleration due to gravity have same dimensional formula.

Gravitational acceleration on the surface of a planet is $\frac{{\sqrt 6 }}{{11}}\mathrm{\;}g,\;$, where $g$ is the gravitational acceleration on the surface of earth. The average mass density of the planet is $\frac{2}{3}$ times
that of the earth. If the escape speed on the surface of the earth is taken on be $11\mathrm{\;km}{\mathrm{s}^{ - 1}},$
the escape speed on the surface of the planet in $\mathrm{km}{\mathrm{s}^{ - 1}}\mathrm{\;}$ will be

Find the velocity of escape at the earth given that its radius is $6.4 \times 10^6 \mathrm{~m}$ and the value of $g$ at its surface is $9.8 \mathrm{~ms}^{-2}$.

A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him?

A satellite is orbiting around the earth with orbital radius $R$ and time period $T$. The quantity which remain constant is

Two point masses $2\,g$ and $10\,g$ are separated by $10cm$. The gravitational potential energy of system is

The acceleration due to gravity at height $h$ above the earth if $h < < R$ (Radius of earth) is given by

The largest and the shortest distance of the earth from the sun are ${r_1}\,and\,{r_2}$, its distance from the sun when it is at the perpendicular to the major axis of the orbit drawn from the sun

A particle is projected from earth with speed less than the escape speed. The sum of $KE$ and $PE$ of particle is

A spring balance is graduated on sea level. If a body is weighed with this balance at consecutively increasing heights from earth’s surface, the weight indicated by the balance

An interstellar spacecraft far away from the influence of any star or planet is moving at high speed under the influence of fusion rockets (due to thrust exerted by fusion rockets, the spacecrafts is accelerating). Suddenly the engine malfunctions and stops. The spacecraft will

Assertion: If value of acceleration due to gravity of a planet is lesser than earth then escape velocity from planet is lesser too.
Reason: Escape velocity just depends only on acceleration due to gravity.

In an experiment, a boy draws graph between $v^2(y-$ axis) and ${a}^2$ (x-axis) (where ${v}=$ velocity and ${a}=$ tangential acceleration) for a simple pendulum. The graph is found to be a straight line of negative slope making an angle of $30^{\circ}$ (with ${x}$-axis) when experiment was done on the ground and $60^{\circ}$ (with ${x}$ axis) when experiment was done at height $h$ above the ground. Then $h$ must be $({R}=$ radius of earth $)$

The geostationary orbit of the earth is at a distance of about $36000 \mathrm{~km}$ from the earth's surface. Find the weight of a $120-\mathrm{kg}$ equipment placed in a geostationary satellite. The radius of the earth is $6400 \mathrm{~km}$.

An artificial satellite circled around the earth at a distance of $3400 \mathrm{~km}$. Calculate its orbital velocity and period of revolution. Radius of earth $=6400 \mathrm{~km}$ and $g=9.8 \mathrm{~ms}^{-2}$.

A satellite in its orbit around earth is weightless on account of its

Find the unit of the ratio of magnitude of gravitational intensity and gravitational force:-

For a satellite moving in an orbit around the planet, the ratio of magnitude of potential energy to kinetic energy is

Assertion: Planet is heavenly body revolving round the sun.

Reason: Star is luminous body made of gaseous material.

If the distance between two masses is doubled, the gravitational attraction between them

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 acceleration due to gravity increase by $0.5\%$ when we go from the equator to the poles. What will be the time period of the pendulum at the equator which beats seconds at the poles?

A particle of mass $1 \mathrm{~kg}$ is kept on the surface of a uniform sphere of mass $20 \mathrm{~kg}$ and radius $1.0 \mathrm{~m}$. Find the work to be done against the gravitational force between them to take the particle away from the sphere.

Comets moves around the Sun in a highly elliptical orbit. The gravitational force on the comet due to the Sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every orbit of the comet is zero. Why?

A rocket is intended to leave the Earth’s gravitational field. The
fuel in its main engine is a little less than the amount that is
necessary and an auxiliary engine, (only capable of operating
for a short time) has to be used as well. When is it best to switch
on: the auxiliary engine?

A body of mass $M$ is divided into two parts of masses $m$ and $(M-m)$. If they are kept at a constant distance, then the relation between $m$ and $M$ for maximum force of attraction between them, will be