Gravitation practice · Mixed difficulty

The binding energy of a particle of mass $m$ with a planet, when it is on the planets surface, is $\frac{1}{2} \mathrm{mv}_0^2$. A tunnel is dug along a diameter of the planet and the particle is dropped into it from the surface, when the body reaches the centre of the planet, its speed is

A spherical planet has uniform density $\frac{\pi }{2} \times {10^4}\frac{{kg}}{{{m^3}}}$ . Find out the minimum period for a satellite in a circular orbit around it in seconds. $\left[ {use\,\,G = \frac{{20}}{3} \times {{10}^{ - 11}}\frac{{N - {m^2}}}{{k{g^2}}}} \right]$

Statement I: Earth continuously attracts the moon towards its centre and yet the moon does not move towards the centre of earth.

Statement II: The gravitational force of atteraction between the moon and earth provides the necessary centripetal force.

A geostationary satellite is orbiting the earth at a height of $5R$ above the surface of the earth, $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is

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

Assertion: The magnitude of gravitational potential at the surface of solid sphere is less than that of the centre of sphere.
Reason: Due to solid sphere, gravitational potential is same within the sphere.

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

Statement-1: Orbiting satellite or body has K.E. of always less than that of Potential energy.
Statement-2: For any bound state, the magnitude of potential energy is always twice that of kinetic energy (K.E.)

If the speed of rotation of earth about its axis increases, then the weight of the body at the equator will

The escape velocity for a body projected vertically upwards from the surface of earth is $11\;\mathrm{km}{\mathrm{s}^{ - 1}}$. If the body is projected at an angle of ${45^0}$ with the vertical, the escape velocity will be

A particle of mass $10 \mathrm{~g}$ is kept on the surface of a uniform sphere of mass $100 \mathrm{~kg}$ and radius $10 \mathrm{~cm}$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (you may take $\mathrm{G}=6.67 \times 10^{-11} \mathrm{Nm}^2 / \mathrm{kg}^2$ )

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5 \mathrm{~km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x \frac{G M_e m}{21 R_e}$. The value of $x$ is (take $\left.{R}_{{e}}=6370 \mathrm{~km}\right)$:

In a satellite, if the time period of revolution is $T$, then kinetic energy is proportional to

Assertion: If a particle projected horizontally just above the surface of earth with a speed greater than escape speed, then it will escape from gravitational influence of earth.
Reason: Escape velocity is independent of its direction.

Spot the wrong statement:
The acceleration due to gravity 'g' decreases if

If ${g_e},\;{g_h}\,and\,{g_d}$ be the accelerations due to gravity at earth’s surface, a height $h$ and at depth $d$ respectively. Then

The earth is an approximate 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 body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$. and the other mass, in a circular orbit of radius $\frac{3 R}{2}$. The difference between the final and initial total energies is :

The depth from the surface of the earth of radius $R$ at which the acceleration due to gravity will be $75\%$ of the value on the surface of the earth is

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

A cyclist turns around a curve at 15 miles/hour. If the turns at double the speed, the tendency to overturn is

A body is projected vertically upwards from the surface of Earth with a velocity sufficient enough to carry it to infinity. The time taken by it to each height $h$ is.......s.

Weight of body is maximum at:

If gravitational force on a body of mass 1.5 kg at point is 45N, then the intensity of the gravitational field at that point is

Statement(A): For Geostationary
satellites, height above the earth is
about 35,800 km.

Statement(B): For Polar satellites,
height above the earth is about 500 to
800 km.

Statement(C): For Geostationary
satellites, T = 24 hours.

Statement(D): For Polar satellites, time
period is around 100 minutes.

What is the shortest possible period of an Earth satellite in circular orbit?

What is the distance of a geostationary satellite from the Earth's centre?

A projectile is fired upwards from the surface of the earth with a velocity $k{V_e}$ where ${V_e}$ is the escape and $K < 1$. If r is the maximum distance from the center of the earth to which it rises and R is the radius of the earth then r equals

Earth binds the atmosphere because of

${g_e}\,and\,{g_p}$ denote the acceleration due to gravity on the surface of the earth and another planet whose mass and radius are twice to that of the earth, then