Gravitation practice · Medium

The correct option 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

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

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

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

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 :

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

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

Earth binds the atmosphere because of

If orbital velocity of planet is given by $v = {G^a}{M^b}{R^c}$, then

A satellite is moving around the earth in a circular orbit. The following statements are given

(i)It is moving with a constant velocity.

(ii) It suffers no acceleration.

(iii) Its angular momentum w.r.t. the earth remains conserved.

(iv) Its distance from centre must be equal to $\sqrt{2}$ times of earth's radius.

The correct option is

Gravitational potential on the surface of earth is (M=mass of the earth, R= radius of earth)

Orbital velocity of an artificial does not depend upon

A space ship moves from earth to moon and back. The greatest energy required for the space ship is to overcome the difficulty in

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 centripetal acceleration of a body moving in a circle of radius 100 m with a time period of 2 s will be

A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

Assertion: The work done to project a body of mass $m$ from the earth's surface (radius $R$ ) to infinity is $m g R$.

Reason: The required work done is equal to change in potential energy of the mass, which is equal to $G M m / R$.

If ${v_e}\,and\,{v_o}$ represent escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R, then

The gravitational force between two point masses ${m_1}\,and\,{m_2}$ at separation $r$ is given by $F = k\frac{{{m_1}{m_2}}}{{{r^2}}}$. The constant $k$

Statement 1: Value of acceleration due to gravity is same at all the points inside earth assuming it to be made up of uniform density.
Statement 2: Value of gravitational field increases as we go towards centre in a uniform spherical shell.