Gravitational force exerted by one body on the other. Does Gravitational force obey principle of superposition ? What will be gravitational force exerted by a distribution of mass on another distribution of mass ? Is there a lower limit in space to the gravitational force ?

Find the gravitational force exerted by a Uniform Circular Ring on a point mass lying on its axis.

Find the gravitational force exerted by a uniform shell on a point mass, lying

a) outside the shell

b) inside the shell

Find the Gravitational force exerted by a uniform solid sphere on a point mass lying at a distance r from its center

Gravitation near Earth. Is Earth a perfect sphere ?

Determine the speed with which the earth has to rotate about its axes, so that an object on the equator

a) would be weightless

b) would weigh 1/2 of his actual weight

Take the equilateral radius of Earth = 6400 km.

Gravitational Potential Energy between two bodies. Gravitational Potential Energy of a system of bodies.

Escape speed is the speed with which an object be projected from the surface of a planet so that it never comes back. Does escape speed depend on the angle or path of projection ? What is Binding energy ?

What will be the acceleration due to gravity on the surface of the moon if its radius were (1/4th) the radius of the earth and its mass is (1/80th) of the mass of the earth?

What will be the escape velocity on the surface of the moon if it is 11.2 km/s on the surface of the earth?

What determines the speed and Time period of a planet revolving around Sun ?

The moon goes round the earth in a nearly circular orbit of radius 3.84 105 km in 27.3 days. Determine the mass of the earth from the data provided.

A satellite which appears to stationery wrt the surface of Earth is called a Geostationary satellite. So a geostationary satellite is always above a fixed point on the surface of Earth.

What will be the height of a geostationary satellite above the surface of Earth? What is its orbital speed in this orbit?

Relation between the Mechanical, Kinetic and Potential energies of a revolving planet.

A space-ship is launched into a circular orbit close to earths surface. What additional velocity has now to be imparted to the space-ship in the orbit to overcome the gravitational pull ? ( Radius of the earth = 6400 km, g = 9.8 m/s2 )

A satellite is orbiting close to the surface of Earth. A particle is to be projected from the satellite to just escape from the earth. The escape speed from the earth is ve.

Its speed with respect to the satellite

a) will be less than ve

b) will be more than ve

c) will be equal to ve

d) will depend on direction of projection.

Keplers Laws

Three satellites, of equal masses, are orbiting around Earth in the orbits with the same semi-major axis, as shown in figure. Which of the following is the same for all the satellites,

a) Time Period

b) Total Mechanical Energy

c) Binding Energy

d) Angular Momentum

What is a Field ? What is a Gravitational Field ? Do fields obey principle of Superposition ?

What is Potential ? What is Gravitational Potential ? Is potential absolute or always relative ?

Find the gravitational potential due to a thin ring at a point on its axis.

Find the gravitational potential due to a thin uniform shell.

Find the gravitational potential due to uniforn solid sphere.

Relation between Field and Potential

Energy required to assemble an extended object of mass M is called the Gravitational Self Energy of the object.

Three identical bodies of mass m are located at the vertices of an equilateral triangle with side l. At what speed must they move if they all revolve under the influence of one anothers gravity in a circular orbit circumscribing the triangle while still preserving the equilateral triangle?

A solid sphere has mass M and radius R. A spherical hollow cavity is dug out from it. Its boundary passing through the centre also touches the boundary of the solid sphere. Deduce the gravitational force on a mass m, which is at a distance r from O along the lines of centres.

Two masses m1 and m2 at an infinite distance from each other and initially at rest, start interacting gravitationally. Find their velocity of approach when they are at a distance r apart.

Imagine a light planet revolving around a very massive star in a circular orbit of radius r with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to , then square of the time period will be proportional to

A double star (a system of two stars moving around the center of inertia of the system due to gravitation) has a mass M and its period of revolution is T.

Find the distance between the components of the double star.

Two satellites are moving round the earth in common plane in circular orbits of radii r1 and r2. What time interval separates the periodic approaches of the satellites to each other over the minimum distance?

Two satellites S1 and S2 revolve around a planet in coplanar circular orbit in the same sense. Their periods of revolution are 1 hour and 8 hour respectively. The radius of the orbit of S1 is 104 km. When S2 is closest to S1 find :

a) the speed of S2 relative to S1

b) the angular speed of S2 actually observed by an astronaut in S1.

A planet of mass m moves an elliptical orbit round the sun of mass M so that its farthest and the nearest distances from the sun are r1 and r2 respectively. Find

a) the angular momentum of the planet about the centre of the sun

b) Show that the total mechanical energy of the system depends only on the semi-major axis of the ellipse.

A satellite is put in an orbit just above the earths atmosphere with a velocity 1.5 times the velocity for a circular orbit at that height. The initial velocity is parallel to the surface.

What should be the maximum distance of the satellite from the earth ?

A satellite is orbiting in a circular orbit of radius 2Re about the earth. It is desired to transfer the vehicle to a new circular orbit of radius 4Re. What is the change in the velocity required at the smaller and larger orbits ? Assume that the transfer path is tangential to the orbits. (g = 10m/s2 , Re = 6400km)

A planet P moves in an elliptical orbit round the sun. At the instant when its distance from the sun was ro, its velocity was vo and the angle between the radius vector ro and the velocity vector vo was equal to q. Find the maximum and the minimum distances of the planet from the sun during its motion.

Find the gravitational force between a point mass and a uniform rod of length L in the two positions shown in the figure.

Find the gravitational force on the rod of mass Mr and length equal to the radius of Earth, placed vertically over the surface of Earth.

Find the Center of Gravity of the rod

A tunnel is dug along a diameter of the Earth and a ball of mass m dropped in it. Examine the motion of the ball as it moves in the tunnel.

Find the time taken by the ball to reach the center of Earth

A particle of mass m is projected in the vertically upward direction from the earth?s surface with a velocity that is just sufficient to carry it to infinity. Prove that the time taken by it in reaching height h is where R is the radius of the earth.

A point mass m is placed at a distance of x from the center of a ring of mass M and radius R on the axis of the ring.

Find the value of x, for which the gravitational force exerted by the ring is maximum?

Is the gravitational potential maximum at this point ?

The mass M of a planet is uniformly distributed over a spherical volume of radius R. Calculate the energy needed to de-assemble the planet against the gravitational pull of its Constituent particles.

Given, MR = 2.5 ? 1031 kg. m and g = 10 m/s2.

An artificial satellite revolves around a planet in a circular orbit whose initial radius is n times the radius of the planet. Assuming that the satellite experiences a resistive force due to cosmic dust that depends upon the velocity v of the satellite as F = kv2 where k is a constant

How long the satellite will stay in the orbit until it falls on to the surface of planet.

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