B M Sharma Solutions for Chapter: Gravitation, Exercise 5: CONCEPT APPLICATION EXERCISE

Air friction increases the velocity of the satellite. Explain.

Two satellites move along a circular orbit in the same direction at a small distance from each other. A container has to be thrown from the first satellite on the second one. When will the container reach the second satellite earlier, if it is thrown in the direction of motion of the first satellite or in the opposite direction? The velocity of the container is small in comparison to that of the satellite.

Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. They collide inelastically and stick together as wreckage. Obtain the total energy of the system before and just after the collision. Describe the subsequent motion of the wreckage.

If a satellite is revolving around a planet of mass $M$ in an elliptical orbit of semi-major axis $a.$ Show that the orbital speed of the satellite when it is at a distance $r$ from the planet will be given by $v^2=GM\left[\frac{2}{r}-\frac{1}{a}\right].$

An artificial satellite is in a circular orbit at $500 \mathrm{km}$ above the earth's surface.

(i) What is the acceleration of the satellite?

(ii) What is the acceleration due to gravity at any point along the satellite's path?

Take radius of the earth as $6.5\times {10}^6 \mathrm{m}.$

A satellite of mass $m$ moves in a circular orbit of radius $r$ around the earth. Calculate the total energy required to place the satellite in the orbit from the earth's surface. Assuming initially it to be at rest.

A satellite is lifted from earth to a height $h.$ Let the work done by the external agent be $W_1.$ Then it is projected with a speed $v$ so as to move in a circular orbit doing an extra work $W_2.$ Compare these works done.

An artificial satellite is moving in a circular orbit around the Earth with a speed equal to half the magnitude of escape velocity from the Earth.
(a) Determine the height of the satellite above the Earth's surface.
(b) If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, find the speed with which it hits and surface of Earth.

Given $M=$Mass of Earth & $R=$Radius of earth.